What Do You Know About Divisibility Tests?

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What Do You Know About Divisibility Tests? - Quiz

A divisibility rule is a shorthand way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits. Although there are divisibility tests for numbers in any radix, or base, and they are all different, this article presents rules and examples only for decimal, or base 10, numbers. Martin Gardner explained and popularized these rules in his September 1962 "Mathematical Games" column in Scientific American.


Questions and Answers
  • 1. 

    Who explained and popularized divisibility rules?

    • A. 

      Martin Gardner

    • B. 

      Abraham Lincoln

    • C. 

      Isaac Newton

    • D. 

      Albert Einstein

    Correct Answer
    A. Martin Gardner
    Explanation
    Martin Gardner is the correct answer because he was a popular American mathematics and science writer who explained and popularized many mathematical concepts, including divisibility rules. He wrote numerous books and articles on recreational mathematics, making complex mathematical ideas accessible and enjoyable for a wide audience. His work had a significant impact on the popularization and understanding of mathematics, making him a well-known figure in the field.

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  • 2. 

    Martin Gardner explained and popularized these rules in?

    • A. 

      June 1997

    • B. 

      September 1962

    • C. 

      July 1999

    • D. 

      May 1964

    Correct Answer
    B. September 1962
    Explanation
    In September 1962, Martin Gardner explained and popularized these rules.

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  • 3. 

    Divisibility by seven can be tested by what?

    • A. 

      Addition

    • B. 

      Subtraction

    • C. 

      Multiplication

    • D. 

      Division

    Correct Answer
    C. Multiplication
    Explanation
    Divisibility by seven can be tested by multiplication. This is because there is a rule that states if a number is divisible by seven, then its multiples are also divisible by seven. By multiplying a given number by different integers, we can check if the resulting numbers are divisible by seven. If they are, then the original number is also divisible by seven.

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  • 4. 

    The Pohlman–Mass method provides a quick solution that can determine if most integers are divisible by .....?

    • A. 

      Seven in three steps or less

    • B. 

      Four in two steps or less

    • C. 

      Six in three steps or more

    • D. 

      Eight in two steps or less

    Correct Answer
    A. Seven in three steps or less
    Explanation
    The Pohlman-Mass method is a quick solution to determine if most integers are divisible by seven in three steps or less. This method is efficient and can be used to quickly identify if a number is divisible by seven without having to perform lengthy calculations.

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  • 5. 

    Divisibility by 6 is determined by checking the original number to see if it is both an ....?

    • A. 

      Odd number

    • B. 

      Even number

    • C. 

      Denominator number

    • D. 

      Numeral number

    Correct Answer
    B. Even number
    Explanation
    Divisibility by 6 is determined by checking if the original number is both an even number and divisible by 3. This is because 6 is a multiple of both 2 and 3. If a number is even, it is divisible by 2, and if it is divisible by 3, it will also be divisible by 6. Therefore, for a number to be divisible by 6, it must be an even number.

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  • 6. 

    Divisibility by 5 is easily determined by checking the last digit in the number (475), and seeing if it is either ....?

    • A. 

      0 or 1

    • B. 

      2 or 4

    • C. 

      1 or 3

    • D. 

      0 or 5

    Correct Answer
    D. 0 or 5
    Explanation
    Divisibility by 5 is easily determined by checking the last digit in the number. If the last digit is either 0 or 5, then the number is divisible by 5. This is because any number that ends in 0 or 5 is a multiple of 5. Therefore, the correct answer is 0 or 5.

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  • 7. 

    If the last number is either 0 or 5, the entire number is divisible by ....?

    • A. 

      5

    • B. 

      4

    • C. 

      3

    • D. 

      2

    Correct Answer
    A. 5
    Explanation
    If the last digit of a number is either 0 or 5, it means that the number is divisible by 5. This is because any number ending in 0 or 5 is a multiple of 5. Therefore, the entire number is divisible by 5.

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  • 8. 

    Also, in divisibility by 5, if the last digit in the number is 0, then the result will be the remaining digits multiplied by ...?

    • A. 

      1

    • B. 

      2

    • C. 

      4

    • D. 

      3

    Correct Answer
    B. 2
    Explanation
    In divisibility by 5, if the last digit in the number is 0, then the result will be the remaining digits multiplied by 2. This is because any number that ends with 0 is divisible by 5, and when we divide it by 5, the result will be the remaining digits multiplied by 2.

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  • 9. 

    No special condition. Any integer is divisible by ...?

    • A. 

      1

    • B. 

      6

    • C. 

      7

    • D. 

      2

    Correct Answer
    A. 1
    Explanation
    Any integer is divisible by 1 because division by 1 results in the number itself. In other words, any number divided by 1 equals the same number. Therefore, any integer can be evenly divided by 1 without leaving a remainder.

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  • 10. 

    Divisibility rule is a subject under which course?

    • A. 

      Biology

    • B. 

      Maths

    • C. 

      Music

    • D. 

      Government

    Correct Answer
    B. Maths
    Explanation
    The correct answer is Maths because divisibility rules are mathematical principles that help determine if a number is divisible by another number without performing the actual division. These rules are taught in mathematics courses to help students understand and apply them in solving mathematical problems involving divisibility.

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