Total number of ways of factorising the number of 676 in to two factors, that are prime to each other is equal to

• A: 2
• B: 4
• C: 1
• D: None of these

To determine the total number of ways to factor the number 676 into two factors that are coprime (meaning they share no common factors other than 1), we first need to find the prime factorization of 676.

Prime Factorization of 676

We can break down 676 as follows:

• 676 = 26 × 26
• 26 = 2 × 13

Thus, the prime factorization of 676 is:

676 = 2^2 × 13^2

Coprime Factors

For two factors to be coprime, they must not share any prime factors. The prime factors of 676 are 2 and 13. We can create coprime pairs by taking one prime factor from each group:

• Factor 1: 1 (which is coprime with any number)
• Factor 2: 676
• Factor 3: 2 (from the prime factorization)
• Factor 4: 338 (which is 676 divided by 2)
• Factor 5: 13 (from the prime factorization)
• Factor 6: 52 (which is 676 divided by 13)

Counting Coprime Pairs

Now, we can list the coprime pairs:

• (1, 676)
• (2, 338)
• (13, 52)

These pairs show that there are three unique combinations where the factors are coprime.

Final Answer

The total number of ways to factor 676 into two coprime factors is 3. Therefore, the answer is D: None of these.