# What is the Greatest Common Factor of 98 and 114?

Greatest common factor (GCF) of 98 and 114 is **2**.

GCF(98,114) = 2

We will now calculate the prime factors of **98 and 114**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 98 and 114.

## How to find the GCF of 98 and 114?

We will first find the prime factorization of 98 and 114. After we will calculate the factors of 98 and 114 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 114

Prime factors of 114 are 2, 3, 19. Prime factorization of **114** in exponential form is:

114 = 2^{1} × 3^{1} × 19^{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 114

List of positive integer factors of 114 that divides 98 without a remainder.

1, 2, 3, 6, 19, 38, 57

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 98 and 114. The biggest common factor number is the **GCF** number.

So the **greatest common factor 98 and 114** is **2**.

Also check out the Least Common Multiple of 98 and 114

#### Related Greatest Common Factors of 98

- GCF of 98 and 102
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- GCF of 98 and 113
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#### Related Greatest Common Factors of 114

- GCF of 114 and 118
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- GCF of 114 and 130
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- GCF of 114 and 132
- GCF of 114 and 133
- GCF of 114 and 134