What is the Greatest Common Factor of 10214 and 10220?

Greatest common factor (GCF) of 10214 and 10220 is 2.

GCF(10214,10220) = 2

We will now calculate the prime factors of 10214 and 10220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10214 and 10220.

How to find the GCF of 10214 and 10220?

We will first find the prime factorization of 10214 and 10220. After we will calculate the factors of 10214 and 10220 and find the biggest common factor number .

Step-1: Prime Factorization of 10214

Prime factors of 10214 are 2, 5107. Prime factorization of 10214 in exponential form is:

10214 = 2¹ × 5107¹

Step-2: Prime Factorization of 10220

Prime factors of 10220 are 2, 5, 7, 73. Prime factorization of 10220 in exponential form is:

10220 = 2² × 5¹ × 7¹ × 73¹

Step-3: Factors of 10214

List of positive integer factors of 10214 that divides 10214 without a remainder.

1, 2, 5107

Step-4: Factors of 10220

List of positive integer factors of 10220 that divides 10214 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 73, 140, 146, 292, 365, 511, 730, 1022, 1460, 2044, 2555, 5110

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10214 and 10220. The biggest common factor number is the GCF number.
So the greatest common factor 10214 and 10220 is 2.

Also check out the Least Common Multiple of 10214 and 10220