# What is the Greatest Common Factor of 98 and 112?

Greatest common factor (GCF) of 98 and 112 is **14**.

GCF(98,112) = 14

We will now calculate the prime factors of **98 and 112**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 98 and 112.

## How to find the GCF of 98 and 112?

We will first find the prime factorization of 98 and 112. After we will calculate the factors of 98 and 112 and find the biggest common factor number .

### Step-1: Prime Factorization of 98

Prime factors of 98 are 2, 7. Prime factorization of **98** in exponential form is:

98 = 2^{1} × 7^{2}

### Step-2: Prime Factorization of 112

Prime factors of 112 are 2, 7. Prime factorization of **112** in exponential form is:

112 = 2^{4} × 7^{1}

### Step-3: Factors of 98

List of positive integer factors of 98 that divides 98 without a remainder.

1, 2, 7, 14, 49

### Step-4: Factors of 112

List of positive integer factors of 112 that divides 98 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 98 and 112. The biggest common factor number is the **GCF** number.

So the **greatest common factor 98 and 112** is **14**.

Also check out the Least Common Multiple of 98 and 112

#### Related Greatest Common Factors of 98

- GCF of 98 and 102
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#### Related Greatest Common Factors of 112

- GCF of 112 and 116
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