What is the Greatest Common Factor of 10102 and 10106?

Greatest common factor (GCF) of 10102 and 10106 is 2.

GCF(10102,10106) = 2

We will now calculate the prime factors of 10102 and 10106, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10102 and 10106.

How to find the GCF of 10102 and 10106?

We will first find the prime factorization of 10102 and 10106. After we will calculate the factors of 10102 and 10106 and find the biggest common factor number .

Step-1: Prime Factorization of 10102

Prime factors of 10102 are 2, 5051. Prime factorization of 10102 in exponential form is:

10102 = 2¹ × 5051¹

Step-2: Prime Factorization of 10106

Prime factors of 10106 are 2, 31, 163. Prime factorization of 10106 in exponential form is:

10106 = 2¹ × 31¹ × 163¹

Step-3: Factors of 10102

List of positive integer factors of 10102 that divides 10102 without a remainder.

1, 2, 5051

Step-4: Factors of 10106

List of positive integer factors of 10106 that divides 10102 without a remainder.

1, 2, 31, 62, 163, 326, 5053

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10102 and 10106. The biggest common factor number is the GCF number.
So the greatest common factor 10102 and 10106 is 2.

Also check out the Least Common Multiple of 10102 and 10106