What is the Greatest Common Factor of 2742 and 2760?

Greatest common factor (GCF) of 2742 and 2760 is 6.

GCF(2742,2760) = 6

We will now calculate the prime factors of 2742 and 2760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2742 and 2760.

How to find the GCF of 2742 and 2760?

We will first find the prime factorization of 2742 and 2760. After we will calculate the factors of 2742 and 2760 and find the biggest common factor number .

Step-1: Prime Factorization of 2742

Prime factors of 2742 are 2, 3, 457. Prime factorization of 2742 in exponential form is:

2742 = 2¹ × 3¹ × 457¹

Step-2: Prime Factorization of 2760

Prime factors of 2760 are 2, 3, 5, 23. Prime factorization of 2760 in exponential form is:

2760 = 2³ × 3¹ × 5¹ × 23¹

Step-3: Factors of 2742

List of positive integer factors of 2742 that divides 2742 without a remainder.

1, 2, 3, 6, 457, 914, 1371

Step-4: Factors of 2760

List of positive integer factors of 2760 that divides 2742 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 23, 24, 30, 40, 46, 60, 69, 92, 115, 120, 138, 184, 230, 276, 345, 460, 552, 690, 920, 1380

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2742 and 2760. The biggest common factor number is the GCF number.
So the greatest common factor 2742 and 2760 is 6.

Also check out the Least Common Multiple of 2742 and 2760