Question 30

90 has 6 and 15 as factors.

The number 90 is divisible by both 6 and 15, making this statement true. When multiplied, 6 × 15 equals 90, confirming that they are indeed factors of the number.

A) It has 10 as a multiple

This statement is incorrect because a multiple of a number is obtained by multiplying that number by an integer. While 10 is a factor of 90, the statement is misleading as it does not accurately describe the relationship between 10 and 90.

B) It has 6 and 15 as factors

This statement is true. Both 6 and 15 divide evenly into 90, with 90 being the product of 6 × 15. Therefore, 6 and 15 are valid factors of the number.

C) It has four distinct prime factors

This statement is incorrect. The prime factorization of 90 is 2 × 3 × 3 × 5, which includes only three distinct prime factors: 2, 3, and 5. Thus, it does not have four distinct prime factors.

D) It is divisible by 9 but not by 18

This statement is incorrect. The number 90 is divisible by both 9 and 18, as 90 ÷ 9 equals 10 and 90 ÷ 18 equals 5. Therefore, stating that it is not divisible by 18 is false.

Conclusion

The correct answer is that 90 has 6 and 15 as factors, as they both evenly divide into 90. All other options are incorrect based on the definitions of multiples, factors, and the properties of prime factorization. This highlights the importance of understanding the relationships between numbers in basic arithmetic.