If a number is a multiple of both 8 and 14, which of the following numbers is gu

₹0.0

Question: If a number is a multiple of both 8 and 14, which of the following numbers is guaranteed to be a factor of that number? (2023)

Options:

Correct Answer: 2

Exam Year: 2023

Solution:

Since any multiple of 8 and 14 must also be a multiple of their GCD, which includes 2 as a factor.

If a number is a multiple of both 8 and 14, which of the following numbers is guaranteed to be a factor of that number? (2023)

If a number is a multiple of both 8 and 14, which of the following numbers is guaranteed to be a factor of that number? (2023)

Step 1: Understand what a multiple is. A multiple of a number is the result of multiplying that number by an integer.
Step 2: Identify the numbers in the question: 8 and 14.
Step 3: Find the greatest common divisor (GCD) of 8 and 14. The GCD is the largest number that divides both numbers without leaving a remainder.
Step 4: Calculate the GCD of 8 and 14. The factors of 8 are 1, 2, 4, 8 and the factors of 14 are 1, 2, 7, 14. The common factors are 1 and 2, so the GCD is 2.
Step 5: Understand that any number that is a multiple of both 8 and 14 must also be a multiple of their GCD (which is 2).
Step 6: Conclude that since the GCD is 2, any number that is a multiple of both 8 and 14 will definitely have 2 as a factor.

Multiples and Factors – Understanding that a number that is a multiple of two other numbers must also be a multiple of their greatest common divisor (GCD).
Greatest Common Divisor (GCD) – The GCD of two numbers is the largest number that divides both of them without leaving a remainder.