Question 29

It has 6 and 15 as factors.

The number 90 can be factored into 6 and 15, which are both whole numbers that can be multiplied together to yield 90. This confirms that 6 and 15 are indeed factors of 90.

A) It has 10 as a multiple.

This statement is incorrect because while 90 does have 10 as a factor (90 = 10 x 9), it is not accurate to say it has 10 as a multiple. Rather, multiples of 10 include numbers like 10, 20, 30, etc., but 90 itself is not a multiple of 10.

B) It has 6 and 15 as factors.

This statement is correct as both 6 and 15 can be multiplied together (6 x 15 = 90) to give the number 90. Therefore, this option accurately describes the relationship of 6 and 15 to the number 90.

C) It has four distinct prime factors.

This statement is incorrect because the prime factorization of 90 is 2, 3, and 5 (90 = 2 x 3^2 x 5). There are only three distinct prime factors, not four.

D) It is divisible by 9 but not by 18.

This statement is incorrect because while 90 is divisible by 9 (90 ÷ 9 = 10), it is also divisible by 18 (90 ÷ 18 = 5). Thus, this option does not accurately represent the divisibility of 90.

Conclusion

The correct answer is option B, as it accurately identifies 6 and 15 as factors of 90. All other options fail to provide correct information regarding the properties of the number 90, making option B the definitive choice in this context.