Question

The greatest common factor of 350 and 825 is

Answer 1

To find the greatest common factor (GCF) of 350 and 825, we can use their prime factorizations.

**Step 1: Prime factorization of 350**

1. Divide by 2:
\( 350 ÷ 2 = 175 \)
2. Divide by 5:
\( 175 ÷ 5 = 35 \)
3. Divide by 5 again:
\( 35 ÷ 5 = 7 \)

Thus, the prime factorization of 350 is:
\[
350 = 2^1 \times 5^2 \times 7^1
\]

**Step 2: Prime factorization of 825**

1. Divide by 3:
\( 825 ÷ 3 = 275 \)
2. Divide by 5:
\( 275 ÷ 5 = 55 \)
3. Divide by 5 again:
\( 55 ÷ 5 = 11 \)

Thus, the prime factorization of 825 is:
\[
825 = 3^1 \times 5^2 \times 11^1
\]

**Step 3: Identify common factors**

The common prime factors of 350 and 825 are:
- \( 5^2 \)

**Step 4: Calculate the GCF**

The GCF is found by taking the lowest power of all common prime factors:
\[
GCF = 5^2 = 25
\]

Therefore, the greatest common factor of 350 and 825 is \(\boxed{25}\).