# What is the Greatest Common Factor of 98 and 102?

Greatest common factor (GCF) of 98 and 102 is **2**.

GCF(98,102) = 2

We will now calculate the prime factors of **98 and 102**, than find the greatest common factor *(greatest common divisor (gcd))* of the numbers by matching the biggest common factor of 98 and 102.

## How to find the GCF of 98 and 102?

We will first find the prime factorization of 98 and 102. After we will calculate the factors of 98 and 102 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 102

Prime factors of 102 are 2, 3, 17. Prime factorization of **102** in exponential form is:

102 = 2^{1} × 3^{1} × 17^{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 102

List of positive integer factors of 102 that divides 98 without a remainder.

1, 2, 3, 6, 17, 34, 51

#### Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 98 and 102. The biggest common factor number is the **GCF** number.

So the **greatest common factor 98 and 102** is **2**.

Also check out the Least Common Multiple of 98 and 102

#### Related Greatest Common Factors of 98

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

- GCF of 102 and 106
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