If the product of two numbers is a multiple of 15, which of the following must b

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Question: If the product of two numbers is a multiple of 15, which of the following must be true?

Options:

Correct Answer: At least one of the numbers is a multiple of 5.

Solution:

For the product to be a multiple of 15, at least one of the numbers must be a multiple of 5.

If the product of two numbers is a multiple of 15, which of the following must be true?

If the product of two numbers is a multiple of 15, which of the following must be true?

Step 1: Understand what a multiple of 15 is. A multiple of 15 is any number that can be divided by 15 without leaving a remainder.
Step 2: Factor 15 into its prime factors. 15 can be factored into 3 and 5 (15 = 3 * 5).
Step 3: For a product of two numbers to be a multiple of 15, it must include both prime factors: 3 and 5.
Step 4: Determine how the product can include these factors. This can happen if at least one of the two numbers is a multiple of 3 and at least one is a multiple of 5.
Step 5: Focus on the requirement for the number 5. Since 5 is one of the prime factors of 15, at least one of the two numbers must be a multiple of 5 for their product to be a multiple of 15.

Multiples and Factors – Understanding that a number is a multiple of another if it can be divided by that number without a remainder.
Prime Factorization – Recognizing that 15 can be factored into its prime components, which are 3 and 5.
Product of Numbers – Knowing that the product of two numbers is influenced by the factors of each number.