Sure, let's find the Greatest Common Factor (G.C.F) of 16 and 28.
1. Define the Numbers:
We are working with the numbers 16 and 28.
2. Prime Factorization:
- Find the prime factorization of each number.
- For 16:
- 16 is divisible by 2: 16 ÷ 2 = 8
- 8 is divisible by 2: 8 ÷ 2 = 4
- 4 is divisible by 2: 4 ÷ 2 = 2
- 2 is divisible by 2: 2 ÷ 2 = 1
So, the prime factorization of 16 is [tex]\(2^4\)[/tex].
- For 28:
- 28 is divisible by 2: 28 ÷ 2 = 14
- 14 is divisible by 2: 14 ÷ 2 = 7
- Then, 7 is a prime number.
So, the prime factorization of 28 is [tex]\(2^2 \times 7\)[/tex].
3. Identify Common Factors:
- The only common prime factor between 16 and 28 is 2.
4. Determine the Lowest Power of Common Factors:
- The lowest power of the common factor 2 is [tex]\(2^2\)[/tex] since the factors of 16 include [tex]\(2^4\)[/tex] and 28 include [tex]\(2^2\)[/tex].
5. Calculate the G.C.F:
- The G.C.F is [tex]\(2^2\)[/tex].
The Greatest Common Factor (G.C.F) of 16 and 28 is therefore [tex]\(2^2 = 4\)[/tex].
So, the G.C.F of 16 and 28 is 4.
