Divisibility Test

1) Under which course is the subject of divisibility rules typically studied?

Biology

Maths

Music

Government

Divisibility rules are studied under the course of mathematics. These rules help determine whether one number can be evenly divided by another without performing the actual division. They are fundamental in simplifying calculations and enhancing number sense, particularly useful in topics like arithmetic, algebra, and number theory. Understanding divisibility rules aids in problem-solving and is essential for students learning basic to advanced math. This makes it a key component of mathematics education, unlike subjects like biology, music, or government, where such concepts do not apply.

Explanation

Divisibility rules are studied under the course of mathematics. These rules help determine whether one number can be evenly divided by another without performing the actual division. They are fundamental in simplifying calculations and enhancing number sense, particularly useful in topics like arithmetic, algebra, and number theory. Understanding divisibility rules aids in problem-solving and is essential for students learning basic to advanced math. This makes it a key component of mathematics education, unlike subjects like biology, music, or government, where such concepts do not apply.

2) What number is a whole number divisible by if its last digit is either 0 or 5?

5

4

3

2

A number is divisible by 5 if its last digit is either 0 or 5. This simple rule allows us to quickly check divisibility without performing actual division. For instance, consider the number 45. Since its last digit is 5, it can be evenly divided by 5, resulting in 9 without any remainder. Similarly, if a number ends in 0, like 80, it too can be divided by 5, giving 16 as the result. This rule is very useful in basic arithmetic, helping to simplify calculations and understand number patterns better.

Explanation

A number is divisible by 5 if its last digit is either 0 or 5. This simple rule allows us to quickly check divisibility without performing actual division. For instance, consider the number 45. Since its last digit is 5, it can be evenly divided by 5, resulting in 9 without any remainder. Similarly, if a number ends in 0, like 80, it too can be divided by 5, giving 16 as the result. This rule is very useful in basic arithmetic, helping to simplify calculations and understand number patterns better.

3) Who explained and popularized divisibility rules?

Martin Gardner

Abraham Lincoln

Isaac Newton

Albert Einstein

Martin Gardner, a renowned American popular mathematics and science writer, explained and popularized many mathematical concepts, including divisibility rules. His work in recreational mathematics brought complex mathematical ideas to a wider audience in an accessible and engaging manner. Through his books and columns, Gardner introduced and demystified divisibility rules, making them understandable and applicable for students and enthusiasts. His contributions to popularizing mathematical concepts have left a lasting impact, helping many people develop a deeper appreciation for the beauty and utility of mathematics in everyday life.

Explanation

Martin Gardner, a renowned American popular mathematics and science writer, explained and popularized many mathematical concepts, including divisibility rules. His work in recreational mathematics brought complex mathematical ideas to a wider audience in an accessible and engaging manner. Through his books and columns, Gardner introduced and demystified divisibility rules, making them understandable and applicable for students and enthusiasts. His contributions to popularizing mathematical concepts have left a lasting impact, helping many people develop a deeper appreciation for the beauty and utility of mathematics in everyday life.

4) How is divisibility by 6 determined by checking the original number?

Odd number

Even number

Denominator number

Numeral number

Divisibility by 6 is determined by checking if the original number is both an even number and divisible by 3. To be divisible by 6, the number must satisfy two conditions: it must be even (meaning it ends in 0, 2, 4, 6, or 8) and the sum of its digits must be divisible by 3. This dual check ensures that the number can be evenly divided by both 2 and 3, which are the prime factors of 6. For example, the number 24 is even, and the sum of its digits (2 + 4) equals 6, which is divisible by 3, making 24 divisible by 6.

Explanation

Divisibility by 6 is determined by checking if the original number is both an even number and divisible by 3. To be divisible by 6, the number must satisfy two conditions: it must be even (meaning it ends in 0, 2, 4, 6, or 8) and the sum of its digits must be divisible by 3. This dual check ensures that the number can be evenly divided by both 2 and 3, which are the prime factors of 6. For example, the number 24 is even, and the sum of its digits (2 + 4) equals 6, which is divisible by 3, making 24 divisible by 6.

5) How is divisibility by 5 easily determined by checking the last digit in the number?

0 or 1

2 or 4

1 or 3

0 or 5

Divisibility by 5 is easily determined by looking at the last digit of the number. If the last digit is either 0 or 5, the entire number is divisible by 5. This rule simplifies checking divisibility, as you only need to examine the final digit rather than performing lengthy calculations. For instance, in the number 475, the last digit is 5, which means 475 is divisible by 5. This straightforward rule is useful in various mathematical applications and helps in quickly identifying multiples of 5.

Explanation

Divisibility by 5 is easily determined by looking at the last digit of the number. If the last digit is either 0 or 5, the entire number is divisible by 5. This rule simplifies checking divisibility, as you only need to examine the final digit rather than performing lengthy calculations. For instance, in the number 475, the last digit is 5, which means 475 is divisible by 5. This straightforward rule is useful in various mathematical applications and helps in quickly identifying multiples of 5.

6) When did Martin Gardner explain and popularize divisibility rules?

June 1997

September 1962

July 1999

May 1964

Martin Gardner explained and popularized divisibility rules in September 1962. His work often appeared in "Scientific American," where he contributed a long-running column called "Mathematical Games." In these columns, Gardner introduced and elaborated on various mathematical concepts, making them accessible to a broad audience. The September 1962 publication is one of the many instances where he explained the practical use of divisibility rules, thereby helping students and math enthusiasts understand and apply these principles more effectively in their studies and everyday problem-solving.

Explanation

Martin Gardner explained and popularized divisibility rules in September 1962. His work often appeared in "Scientific American," where he contributed a long-running column called "Mathematical Games." In these columns, Gardner introduced and elaborated on various mathematical concepts, making them accessible to a broad audience. The September 1962 publication is one of the many instances where he explained the practical use of divisibility rules, thereby helping students and math enthusiasts understand and apply these principles more effectively in their studies and everyday problem-solving.

7) What number must the remaining digits of a number be multiplied by to find the result of division by 5 if the last digit is 0?

1

2

4

3

When a number ends in 0 and you divide it by 5, you multiply the remaining digits by 2 to find the result. For example, if you have the number 60, you remove the 0 (last digit) and multiply the remaining digit, which is 6, by 2. The result is 12. This is because dividing by 5 is the same as multiplying by 2 and then dividing by 10, which just moves the decimal point one place to the left, simplifying the division.

Explanation

When a number ends in 0 and you divide it by 5, you multiply the remaining digits by 2 to find the result. For example, if you have the number 60, you remove the 0 (last digit) and multiply the remaining digit, which is 6, by 2. The result is 12. This is because dividing by 5 is the same as multiplying by 2 and then dividing by 10, which just moves the decimal point one place to the left, simplifying the division.

8) How can divisibility by seven be tested?

Addition

Subtraction

Multiplication

Division

Divisibility by seven can be tested using a method involving subtraction. To check if a number is divisible by seven, take the last digit of the number, double it, and subtract this value from the rest of the number. If the resulting number is divisible by seven, then the original number is also divisible by seven. This method simplifies the process of checking divisibility for larger numbers without performing long division. For example, with the number 203, doubling the last digit (3) gives 6, and subtracting this from 20 (the rest of the number) results in 14, which is divisible by seven.

Explanation

Divisibility by seven can be tested using a method involving subtraction. To check if a number is divisible by seven, take the last digit of the number, double it, and subtract this value from the rest of the number. If the resulting number is divisible by seven, then the original number is also divisible by seven. This method simplifies the process of checking divisibility for larger numbers without performing long division. For example, with the number 203, doubling the last digit (3) gives 6, and subtracting this from 20 (the rest of the number) results in 14, which is divisible by seven.

9) What number is any integer divisible by without any special conditions?

1

6

7

2

Any integer is divisible by 1 without any special conditions. This is because dividing any number by 1 results in the number itself as the quotient, which means there is no remainder. For instance, dividing 7, 15, or 100 by 1 always gives back 7, 15, and 100 respectively. This rule applies universally to all integers, making 1 a unique divisor. It simplifies the concept of divisibility and helps in understanding the foundational properties of numbers in mathematics.

Explanation

Any integer is divisible by 1 without any special conditions. This is because dividing any number by 1 results in the number itself as the quotient, which means there is no remainder. For instance, dividing 7, 15, or 100 by 1 always gives back 7, 15, and 100 respectively. This rule applies universally to all integers, making 1 a unique divisor. It simplifies the concept of divisibility and helps in understanding the foundational properties of numbers in mathematics.

10) What does the Pohlman–Mass method quickly determine about most integers?

Seven in three steps or less

Four in two steps or less

Six in three steps or more

Eight in two steps or less

The Pohlman–Mass method offers a quick and efficient way to determine if most integers are divisible by seven in three steps or less. This method involves a sequence of simple arithmetic operations that help identify divisibility by seven without extensive calculations. It is particularly useful for large numbers, making the process faster and more straightforward. The method's effectiveness and simplicity make it a valuable tool for quickly checking divisibility, saving time and effort in mathematical problem-solving.

Explanation

The Pohlman–Mass method offers a quick and efficient way to determine if most integers are divisible by seven in three steps or less. This method involves a sequence of simple arithmetic operations that help identify divisibility by seven without extensive calculations. It is particularly useful for large numbers, making the process faster and more straightforward. The method's effectiveness and simplicity make it a valuable tool for quickly checking divisibility, saving time and effort in mathematical problem-solving.