What is the Greatest Common Factor of 27500 and 27514?

Greatest common factor (GCF) of 27500 and 27514 is 2.

GCF(27500,27514) = 2

We will now calculate the prime factors of 27500 and 27514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27500 and 27514.

How to find the GCF of 27500 and 27514?

We will first find the prime factorization of 27500 and 27514. After we will calculate the factors of 27500 and 27514 and find the biggest common factor number .

Step-1: Prime Factorization of 27500

Prime factors of 27500 are 2, 5, 11. Prime factorization of 27500 in exponential form is:

27500 = 2² × 5⁴ × 11¹

Step-2: Prime Factorization of 27514

Prime factors of 27514 are 2, 13757. Prime factorization of 27514 in exponential form is:

27514 = 2¹ × 13757¹

Step-3: Factors of 27500

List of positive integer factors of 27500 that divides 27500 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 55, 100, 110, 125, 220, 250, 275, 500, 550, 625, 1100, 1250, 1375, 2500, 2750, 5500, 6875, 13750

Step-4: Factors of 27514

List of positive integer factors of 27514 that divides 27500 without a remainder.

1, 2, 13757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27500 and 27514. The biggest common factor number is the GCF number.
So the greatest common factor 27500 and 27514 is 2.

Also check out the Least Common Multiple of 27500 and 27514