Ch. 4 Section A Quiz

Explanation
240 is not divisible by 9 because 9 does not evenly divide into 240. When we divide 240 by 9, we get a remainder of 6. Therefore, 240 is not divisible by 9.

Explanation
A prime number is a number that is only divisible by 1 and itself. In the case of 19, it cannot be divided evenly by any other number except for 1 and 19. Therefore, 19 is classified as a prime number.

Explanation
A composite number is a positive integer greater than 1 that has at least one divisor other than 1 and itself. In the case of 51, it can be divided evenly by 3 and 17 in addition to 1 and 51. Therefore, 51 is a composite number.

Explanation
The statement "All even numbers are composite" is false. Even numbers are numbers that can be divided by 2 without leaving a remainder. While some even numbers are indeed composite (such as 4, 6, 8, etc.), there are also even numbers that are prime (such as 2). Prime numbers are only divisible by 1 and themselves, and they are not composite. Therefore, not all even numbers are composite, making the statement false.

Explanation
The statement is false because most of the numbers in our number system are not prime. Prime numbers are numbers that are only divisible by 1 and themselves. However, in our number system, there are only a few prime numbers compared to the total number of numbers. Most numbers are composite, meaning they have multiple factors other than 1 and themselves. Therefore, the correct answer is false.

Explanation
The statement is true because the multiples of 4 can be obtained by multiplying 4 by any whole number. Since 2 is a factor of 4, all multiples of 4 will also be divisible by 2, making them even numbers.

Explanation
A number that ends with a zero or five is not necessarily divisible by 10. Divisibility by 10 requires that a number ends with zero, indicating that it is a multiple of 10. However, a number ending with five is not divisible by 10 as it is only a multiple of 5. Therefore, the statement is false.

Explanation
The factors of a number are the numbers that can divide evenly into that number without leaving a remainder. In this case, we are looking for the factors of 20. By listing all the numbers that can divide evenly into 20, we find that the factors are 1, 2, 4, 5, 10, and 20. These numbers can all divide into 20 without leaving a remainder.

Explanation
The greatest common factor between 12 and 16 is 4 because it is the largest number that can evenly divide both 12 and 16 without leaving a remainder. To find the greatest common factor, we can list the factors of both numbers and identify the largest number that appears in both lists. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 16 are 1, 2, 4, 8, and 16. The largest number that appears in both lists is 4, so the greatest common factor is 4.

Explanation
The prime factorization for 81 is 3 x 3 x 3 x 3. This means that 81 can be expressed as the product of prime numbers, specifically four 3's multiplied together.