What is the Greatest Common Factor of 2744 and 2758?

Greatest common factor (GCF) of 2744 and 2758 is 14.

GCF(2744,2758) = 14

We will now calculate the prime factors of 2744 and 2758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2744 and 2758.

How to find the GCF of 2744 and 2758?

We will first find the prime factorization of 2744 and 2758. After we will calculate the factors of 2744 and 2758 and find the biggest common factor number .

Step-1: Prime Factorization of 2744

Prime factors of 2744 are 2, 7. Prime factorization of 2744 in exponential form is:

2744 = 2³ × 7³

Step-2: 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-3: Factors of 2744

List of positive integer factors of 2744 that divides 2744 without a remainder.

1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 343, 392, 686, 1372

Step-4: Factors of 2758

List of positive integer factors of 2758 that divides 2744 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2744 and 2758. The biggest common factor number is the GCF number.
So the greatest common factor 2744 and 2758 is 14.

Also check out the Least Common Multiple of 2744 and 2758