If the HCF of two numbers is equal to one of the numbers, what can be inferred?

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Question: If the HCF of two numbers is equal to one of the numbers, what can be inferred?

Options:

Correct Answer: One number is a multiple of the other

Solution:

If the HCF is equal to one of the numbers, it means that one number is a multiple of the other.

If the HCF of two numbers is equal to one of the numbers, what can be inferred?

If the HCF of two numbers is equal to one of the numbers, what can be inferred?

Correct Answer: One number is a multiple of the other.

Step 1: Understand what HCF means. HCF stands for Highest Common Factor, which is the largest number that divides both numbers without leaving a remainder.
Step 2: Consider two numbers, let's call them A and B.
Step 3: If the HCF of A and B is equal to A, it means A is the largest number that can divide both A and B.
Step 4: Since A can divide itself, it also means that B must be a smaller number that can be formed by multiplying A by some whole number.
Step 5: Therefore, B is a multiple of A.
Step 6: Similarly, if the HCF is equal to B, then A must be a multiple of B.

Highest Common Factor (HCF) – The HCF of two numbers is the largest number that divides both of them without leaving a remainder.
Multiples – If one number is a multiple of another, it means that the first number can be expressed as the second number multiplied by an integer.