What is the Greatest Common Factor of 5614 and 5628?

Greatest common factor (GCF) of 5614 and 5628 is 14.

GCF(5614,5628) = 14

We will now calculate the prime factors of 5614 and 5628, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5614 and 5628.

How to find the GCF of 5614 and 5628?

We will first find the prime factorization of 5614 and 5628. After we will calculate the factors of 5614 and 5628 and find the biggest common factor number .

Step-1: Prime Factorization of 5614

Prime factors of 5614 are 2, 7, 401. Prime factorization of 5614 in exponential form is:

5614 = 2¹ × 7¹ × 401¹

Step-2: Prime Factorization of 5628

Prime factors of 5628 are 2, 3, 7, 67. Prime factorization of 5628 in exponential form is:

5628 = 2² × 3¹ × 7¹ × 67¹

Step-3: Factors of 5614

List of positive integer factors of 5614 that divides 5614 without a remainder.

1, 2, 7, 14, 401, 802, 2807

Step-4: Factors of 5628

List of positive integer factors of 5628 that divides 5614 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 67, 84, 134, 201, 268, 402, 469, 804, 938, 1407, 1876, 2814

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5614 and 5628. The biggest common factor number is the GCF number.
So the greatest common factor 5614 and 5628 is 14.

Also check out the Least Common Multiple of 5614 and 5628