What is the Greatest Common Factor of 27700 and 27705?

Greatest common factor (GCF) of 27700 and 27705 is 5.

GCF(27700,27705) = 5

We will now calculate the prime factors of 27700 and 27705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27700 and 27705.

How to find the GCF of 27700 and 27705?

We will first find the prime factorization of 27700 and 27705. After we will calculate the factors of 27700 and 27705 and find the biggest common factor number .

Step-1: Prime Factorization of 27700

Prime factors of 27700 are 2, 5, 277. Prime factorization of 27700 in exponential form is:

27700 = 2² × 5² × 277¹

Step-2: Prime Factorization of 27705

Prime factors of 27705 are 3, 5, 1847. Prime factorization of 27705 in exponential form is:

27705 = 3¹ × 5¹ × 1847¹

Step-3: Factors of 27700

List of positive integer factors of 27700 that divides 27700 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 277, 554, 1108, 1385, 2770, 5540, 6925, 13850

Step-4: Factors of 27705

List of positive integer factors of 27705 that divides 27700 without a remainder.

1, 3, 5, 15, 1847, 5541, 9235

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27700 and 27705. The biggest common factor number is the GCF number.
So the greatest common factor 27700 and 27705 is 5.

Also check out the Least Common Multiple of 27700 and 27705