Question

Determine the Highest Common Factor (HCF) of each of the following:
A. 112 ; 325
Hcf =?
=?

Write the hcf in full

Answer 1

To determine the Highest Common Factor (HCF) of 112 and 325, we can use the prime factorization method.

1. **Prime Factorization of 112:**
- 112 can be divided by 2:
- 112 ÷ 2 = 56
- 56 ÷ 2 = 28
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7
- 7 is a prime number.
- Therefore, the prime factorization of 112 is:
\[
112 = 2^4 \times 7^1
\]

2. **Prime Factorization of 325:**
- 325 can be divided by 5 (it ends in 5):
- 325 ÷ 5 = 65
- 65 also ends in 5, so we divide again:
- 65 ÷ 5 = 13
- 13 is a prime number.
- Therefore, the prime factorization of 325 is:
\[
325 = 5^2 \times 13^1
\]

3. **Finding the HCF:**
- Now, we have the prime factorizations:
\[
112 = 2^4 \times 7^1
\]
\[
325 = 5^2 \times 13^1
\]
- The common factors are considered for finding the HCF. However, since 112 and 325 do not have any prime factors in common, their HCF is:

\[
\text{HCF} = 1
\]

Thus, the Highest Common Factor (HCF) of 112 and 325 is **1**.