What is the Greatest Common Factor of 27400 and 27405?

Greatest common factor (GCF) of 27400 and 27405 is 5.

GCF(27400,27405) = 5

We will now calculate the prime factors of 27400 and 27405, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27400 and 27405.

How to find the GCF of 27400 and 27405?

We will first find the prime factorization of 27400 and 27405. After we will calculate the factors of 27400 and 27405 and find the biggest common factor number .

Step-1: Prime Factorization of 27400

Prime factors of 27400 are 2, 5, 137. Prime factorization of 27400 in exponential form is:

27400 = 2³ × 5² × 137¹

Step-2: Prime Factorization of 27405

Prime factors of 27405 are 3, 5, 7, 29. Prime factorization of 27405 in exponential form is:

27405 = 3³ × 5¹ × 7¹ × 29¹

Step-3: Factors of 27400

List of positive integer factors of 27400 that divides 27400 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 137, 200, 274, 548, 685, 1096, 1370, 2740, 3425, 5480, 6850, 13700

Step-4: Factors of 27405

List of positive integer factors of 27405 that divides 27400 without a remainder.

1, 3, 5, 7, 9, 15, 21, 27, 29, 35, 45, 63, 87, 105, 135, 145, 189, 203, 261, 315, 435, 609, 783, 945, 1015, 1305, 1827, 3045, 3915, 5481, 9135

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27400 and 27405. The biggest common factor number is the GCF number.
So the greatest common factor 27400 and 27405 is 5.

Also check out the Least Common Multiple of 27400 and 27405