Determine the Highest Common Factor (HCF) of each of the following:

Question

A. 112 ; 325
125 = 5×5×5
352 = 5×5×13
Hcf =?
=?

HCF=?
=?

Answer 1

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

Step 1: Prime Factorization

For 112:

1. Divide by 2:
   \(112 \div 2 = 56\)
2. Divide by 2:
   \(56 \div 2 = 28\)
3. Divide by 2:
   \(28 \div 2 = 14\)
4. Divide by 2:
   \(14 \div 2 = 7\)
5. Now, 7 is a prime number.

So, the prime factorization of \(112\) is:
\[ 112 = 2^4 \times 7^1 \]

For 325:

1. Divide by 5:
   \(325 \div 5 = 65\)
2. Divide by 5:
   \(65 \div 5 = 13\)
3. Now, 13 is a prime number.

So, the prime factorization of \(325\) is:
\[ 325 = 5^2 \times 13^1 \]

Step 2: Determine the HCF

Now that we have the prime factorization of both numbers, we look for common factors.

• Prime factors of \(112\): \(2^4\) and \(7^1\)
• Prime factors of \(325\): \(5^2\) and \(13^1\)

There are no common prime factors between \(112\) and \(325\).

Thus, the HCF of 112 and 325 is:
\[ \text{HCF} = 1 \]

Conclusion

The Highest Common Factor (HCF) of \(112\) and \(325\) is:
HCF = 1.