Rationale
It has 6 and 15 as factors.
The number 90 can be evenly divided by both 6 and 15, confirming that they are indeed factors of 90. This means that when 90 is divided by either number, the result is a whole number without any remainder.
A) It has 10 as a multiple
While 10 is a multiple of 90, this statement is misleading as it implies the reverse. Instead, 90 is a multiple of 10, meaning that 10 can be evenly multiplied to produce 90, rather than the other way around.
C) It has four distinct prime factors
The prime factorization of 90 is 2 × 3 × 3 × 5, which includes only three distinct prime factors: 2, 3, and 5. Therefore, this statement is false, as it overstates the count of distinct prime factors.
D) It is divisible by 9 but not by 18
This statement is incorrect because 90 is divisible by both 9 and 18. When 90 is divided by 9, the result is 10, and when divided by 18, the result is 5, confirming that 90 is divisible by both numbers.
Conclusion
In summary, the valid statement regarding the number 90 is that it has 6 and 15 as factors, clearly demonstrating its divisibility by these numbers. The other choices either misinterpret the relationships of multiples and factors or inaccurately assess the number of distinct prime factors, reinforcing that understanding the fundamentals of factors and multiples is essential in number theory.
