How do you find the GCF of 98 and 28?

To find the greatest common factor (GCF) of 98 and 28, follow these steps:

Step 1: Find the prime factorization of each number.

Prime factorization of 98:

Divide 98 by the smallest prime number (2): 98 ÷ 2 = 49.
49 is not divisible by 2, so try the next smallest prime number, 3. It is also not divisible by 3.
Try 7 (the next prime number): 49 ÷ 7 = 7.
Since 7 is also a prime number, the prime factorization of 98 is: 98 = 2 × 7 × 7 = 2 × 7².
Prime factorization of 28:

Divide 28 by the smallest prime number (2): 28 ÷ 2 = 14.
Divide 14 by 2 again: 14 ÷ 2 = 7.
Since 7 is a prime number, the prime factorization of 28 is: 28 = 2 × 7 = 2 × 7¹.
Step 2: Identify the common factors.

The prime factors of 98 are 2 and 7.
The prime factors of 28 are 2 and 7.
The common factors are 2 and 7.
Step 3: Multiply the smallest powers of the common factors.

The smallest power of 2 in the prime factorizations is 2¹.
The smallest power of 7 in the prime factorizations is 7¹.
Multiply these: 2¹ × 7¹ = 2 × 7 = 14.
Step 4: Verify the result.

Check if 14 divides both 98 and 28: 98 ÷ 14 = 7 (exact division), 28 ÷ 14 = 2 (exact division).
Since 14 is the largest number that divides both 98 and 28, the GCF is 14.

Answer: The GCF of 98 and 28 is 14.