What is the Greatest Common Factor of 762 and 780?

Greatest common factor (GCF) of 762 and 780 is 6.

GCF(762,780) = 6

We will now calculate the prime factors of 762 and 780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 762 and 780.

How to find the GCF of 762 and 780?

We will first find the prime factorization of 762 and 780. After we will calculate the factors of 762 and 780 and find the biggest common factor number .

Step-1: Prime Factorization of 762

Prime factors of 762 are 2, 3, 127. Prime factorization of 762 in exponential form is:

762 = 2¹ × 3¹ × 127¹

Step-2: Prime Factorization of 780

Prime factors of 780 are 2, 3, 5, 13. Prime factorization of 780 in exponential form is:

780 = 2² × 3¹ × 5¹ × 13¹

Step-3: Factors of 762

List of positive integer factors of 762 that divides 762 without a remainder.

1, 2, 3, 6, 127, 254, 381

Step-4: Factors of 780

List of positive integer factors of 780 that divides 762 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 762 and 780. The biggest common factor number is the GCF number.
So the greatest common factor 762 and 780 is 6.

Also check out the Least Common Multiple of 762 and 780