Question

Which of the following is the highest common factor of 4266, 7848, 9540 ?

• A. 18
• B. 20
• C. 22
• D. 24

Answer 1

Answer:

A. 18

The highest common factor (HCF) of 4266, 7848, and 9540 is 18.

1. Find prime factorizations

To find the highest common factor, first break each number down into its prime factors:

• $4266 = 2 \times 3 \times 3 \times 3 \times 79 = 2^1 \times 3^3 \times 79^1$

• $7848 = 2 \times 2 \times 2 \times 3 \times 3 \times 109 = 2^3 \times 3^2 \times 109^1$

• $9540 = 2 \times 2 \times 3 \times 3 \times 5 \times 53 = 2^2 \times 3^2 \times 5^1 \times 53^1$

2. Identify common bases

Next, find the prime numbers that appear in all three factorizations:

• The common prime bases are $2$ and $3$.

3. Multiply lowest powers

Take the lowest exponent for each common prime base and multiply them together:

• For base $2$, the lowest power is $2^1$.

• For base $3$, the lowest power is $3^2$.

$\text{HCF} = 2^1 \times 3^2 = 2 \times 9 = 18$

The highest common factor of 4266, 7848, and 9540 is 18.