To find the greatest common factor (GCF) of 28 and 49, we can start by determining the prime factorization of each number.
Prime factorization of 28:
- 28 can be divided by 2: \( 28 \div 2 = 14 \)
- 14 can be divided by 2: \( 14 \div 2 = 7 \)
- 7 is a prime number.
So, the prime factorization of 28 is: \[ 28 = 2^2 \times 7^1 \]
Prime factorization of 49:
- 49 can be divided by 7: \( 49 \div 7 = 7 \)
- 7 is a prime number.
So, the prime factorization of 49 is: \[ 49 = 7^2 \]
Identifying the GCF: Now, we look for the common prime factors and take the lowest power of each.
The only common prime factor is 7.
- In 28, the power of 7 is 1 (i.e., \( 7^1 \)).
- In 49, the power of 7 is 2 (i.e., \( 7^2 \)).
The lowest power is \( 7^1 \).
Thus, the GCF of 28 and 49 is: \[ \text{GCF} = 7 \]
Therefore, the greatest common factor of 28 and 49 is 7.
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