If a number is a multiple of 15, which of the following must also be true?

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Question: If a number is a multiple of 15, which of the following must also be true?

Options:

Correct Answer: Both 1 and 2.

Solution:

Since 15 = 3 × 5, any multiple of 15 must also be a multiple of both 3 and 5.

If a number is a multiple of 15, which of the following must also be true?

If a number is a multiple of 15, which of the following must also be true?

Step 1: Understand what a multiple is. A multiple of a number is the result of multiplying that number by an integer (like 1, 2, 3, etc.).
Step 2: Identify the number in the question, which is 15.
Step 3: Factor 15 into its prime factors. 15 can be broken down into 3 and 5 (15 = 3 × 5).
Step 4: Recognize that if a number is a multiple of 15, it can be written as 15 times some integer (like 15, 30, 45, etc.).
Step 5: Since 15 is made up of 3 and 5, any number that is a multiple of 15 will also be divisible by both 3 and 5.
Step 6: Conclude that if a number is a multiple of 15, it must also be a multiple of 3 and a multiple of 5.

Multiples and Factors – Understanding that a multiple of a number is also a multiple of its prime factors.
Prime Factorization – Recognizing that 15 can be broken down into its prime factors, 3 and 5.