What is the Greatest Common Factor of 2698 and 2712?

Greatest common factor (GCF) of 2698 and 2712 is 2.

GCF(2698,2712) = 2

We will now calculate the prime factors of 2698 and 2712, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2698 and 2712.

How to find the GCF of 2698 and 2712?

We will first find the prime factorization of 2698 and 2712. After we will calculate the factors of 2698 and 2712 and find the biggest common factor number .

Step-1: Prime Factorization of 2698

Prime factors of 2698 are 2, 19, 71. Prime factorization of 2698 in exponential form is:

2698 = 2¹ × 19¹ × 71¹

Step-2: Prime Factorization of 2712

Prime factors of 2712 are 2, 3, 113. Prime factorization of 2712 in exponential form is:

2712 = 2³ × 3¹ × 113¹

Step-3: Factors of 2698

List of positive integer factors of 2698 that divides 2698 without a remainder.

1, 2, 19, 38, 71, 142, 1349

Step-4: Factors of 2712

List of positive integer factors of 2712 that divides 2698 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 113, 226, 339, 452, 678, 904, 1356

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2698 and 2712. The biggest common factor number is the GCF number.
So the greatest common factor 2698 and 2712 is 2.

Also check out the Least Common Multiple of 2698 and 2712