What is the Greatest Common Factor of 2758 and 2772?

Greatest common factor (GCF) of 2758 and 2772 is 14.

GCF(2758,2772) = 14

We will now calculate the prime factors of 2758 and 2772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2758 and 2772.

How to find the GCF of 2758 and 2772?

We will first find the prime factorization of 2758 and 2772. After we will calculate the factors of 2758 and 2772 and find the biggest common factor number .

Step-1: Prime Factorization of 2758

Prime factors of 2758 are 2, 7, 197. Prime factorization of 2758 in exponential form is:

2758 = 2¹ × 7¹ × 197¹

Step-2: Prime Factorization of 2772

Prime factors of 2772 are 2, 3, 7, 11. Prime factorization of 2772 in exponential form is:

2772 = 2² × 3² × 7¹ × 11¹

Step-3: Factors of 2758

List of positive integer factors of 2758 that divides 2758 without a remainder.

1, 2, 7, 14, 197, 394, 1379

Step-4: Factors of 2772

List of positive integer factors of 2772 that divides 2758 without a remainder.

1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 18, 21, 22, 28, 33, 36, 42, 44, 63, 66, 77, 84, 99, 126, 132, 154, 198, 231, 252, 308, 396, 462, 693, 924, 1386

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2758 and 2772. The biggest common factor number is the GCF number.
So the greatest common factor 2758 and 2772 is 14.

Also check out the Least Common Multiple of 2758 and 2772