What is the Greatest Common Factor of 5642 and 5648?

Greatest common factor (GCF) of 5642 and 5648 is 2.

GCF(5642,5648) = 2

We will now calculate the prime factors of 5642 and 5648, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5642 and 5648.

How to find the GCF of 5642 and 5648?

We will first find the prime factorization of 5642 and 5648. After we will calculate the factors of 5642 and 5648 and find the biggest common factor number .

Step-1: Prime Factorization of 5642

Prime factors of 5642 are 2, 7, 13, 31. Prime factorization of 5642 in exponential form is:

5642 = 2¹ × 7¹ × 13¹ × 31¹

Step-2: Prime Factorization of 5648

Prime factors of 5648 are 2, 353. Prime factorization of 5648 in exponential form is:

5648 = 2⁴ × 353¹

Step-3: Factors of 5642

List of positive integer factors of 5642 that divides 5642 without a remainder.

1, 2, 7, 13, 14, 26, 31, 62, 91, 182, 217, 403, 434, 806, 2821

Step-4: Factors of 5648

List of positive integer factors of 5648 that divides 5642 without a remainder.

1, 2, 4, 8, 16, 353, 706, 1412, 2824

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5642 and 5648. The biggest common factor number is the GCF number.
So the greatest common factor 5642 and 5648 is 2.

Also check out the Least Common Multiple of 5642 and 5648