What is the Greatest Common Factor of 5365 and 5380?

Greatest common factor (GCF) of 5365 and 5380 is 5.

GCF(5365,5380) = 5

We will now calculate the prime factors of 5365 and 5380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5365 and 5380.

How to find the GCF of 5365 and 5380?

We will first find the prime factorization of 5365 and 5380. After we will calculate the factors of 5365 and 5380 and find the biggest common factor number .

Step-1: Prime Factorization of 5365

Prime factors of 5365 are 5, 29, 37. Prime factorization of 5365 in exponential form is:

5365 = 5¹ × 29¹ × 37¹

Step-2: Prime Factorization of 5380

Prime factors of 5380 are 2, 5, 269. Prime factorization of 5380 in exponential form is:

5380 = 2² × 5¹ × 269¹

Step-3: Factors of 5365

List of positive integer factors of 5365 that divides 5365 without a remainder.

1, 5, 29, 37, 145, 185, 1073

Step-4: Factors of 5380

List of positive integer factors of 5380 that divides 5365 without a remainder.

1, 2, 4, 5, 10, 20, 269, 538, 1076, 1345, 2690

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5365 and 5380. The biggest common factor number is the GCF number.
So the greatest common factor 5365 and 5380 is 5.

Also check out the Least Common Multiple of 5365 and 5380