What is the Greatest Common Factor of 78100 and 78114?

Greatest common factor (GCF) of 78100 and 78114 is 2.

GCF(78100,78114) = 2

We will now calculate the prime factors of 78100 and 78114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78100 and 78114.

How to find the GCF of 78100 and 78114?

We will first find the prime factorization of 78100 and 78114. After we will calculate the factors of 78100 and 78114 and find the biggest common factor number .

Step-1: Prime Factorization of 78100

Prime factors of 78100 are 2, 5, 11, 71. Prime factorization of 78100 in exponential form is:

78100 = 2² × 5² × 11¹ × 71¹

Step-2: Prime Factorization of 78114

Prime factors of 78114 are 2, 3, 47, 277. Prime factorization of 78114 in exponential form is:

78114 = 2¹ × 3¹ × 47¹ × 277¹

Step-3: Factors of 78100

List of positive integer factors of 78100 that divides 78100 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 71, 100, 110, 142, 220, 275, 284, 355, 550, 710, 781, 1100, 1420, 1562, 1775, 3124, 3550, 3905, 7100, 7810, 15620, 19525, 39050

Step-4: Factors of 78114

List of positive integer factors of 78114 that divides 78100 without a remainder.

1, 2, 3, 6, 47, 94, 141, 277, 282, 554, 831, 1662, 13019, 26038, 39057

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78100 and 78114. The biggest common factor number is the GCF number.
So the greatest common factor 78100 and 78114 is 2.

Also check out the Least Common Multiple of 78100 and 78114