What is the Greatest Common Factor of 77500 and 77514?

Greatest common factor (GCF) of 77500 and 77514 is 2.

GCF(77500,77514) = 2

We will now calculate the prime factors of 77500 and 77514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77500 and 77514.

How to find the GCF of 77500 and 77514?

We will first find the prime factorization of 77500 and 77514. After we will calculate the factors of 77500 and 77514 and find the biggest common factor number .

Step-1: Prime Factorization of 77500

Prime factors of 77500 are 2, 5, 31. Prime factorization of 77500 in exponential form is:

77500 = 2² × 5⁴ × 31¹

Step-2: Prime Factorization of 77514

Prime factors of 77514 are 2, 3, 12919. Prime factorization of 77514 in exponential form is:

77514 = 2¹ × 3¹ × 12919¹

Step-3: Factors of 77500

List of positive integer factors of 77500 that divides 77500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 31, 50, 62, 100, 124, 125, 155, 250, 310, 500, 620, 625, 775, 1250, 1550, 2500, 3100, 3875, 7750, 15500, 19375, 38750

Step-4: Factors of 77514

List of positive integer factors of 77514 that divides 77500 without a remainder.

1, 2, 3, 6, 12919, 25838, 38757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77500 and 77514. The biggest common factor number is the GCF number.
So the greatest common factor 77500 and 77514 is 2.

Also check out the Least Common Multiple of 77500 and 77514