What is the Greatest Common Factor of 69675 and 69680?

Greatest common factor (GCF) of 69675 and 69680 is 5.

GCF(69675,69680) = 5

We will now calculate the prime factors of 69675 and 69680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69675 and 69680.

How to find the GCF of 69675 and 69680?

We will first find the prime factorization of 69675 and 69680. After we will calculate the factors of 69675 and 69680 and find the biggest common factor number .

Step-1: Prime Factorization of 69675

Prime factors of 69675 are 3, 5, 929. Prime factorization of 69675 in exponential form is:

69675 = 3¹ × 5² × 929¹

Step-2: Prime Factorization of 69680

Prime factors of 69680 are 2, 5, 13, 67. Prime factorization of 69680 in exponential form is:

69680 = 2⁴ × 5¹ × 13¹ × 67¹

Step-3: Factors of 69675

List of positive integer factors of 69675 that divides 69675 without a remainder.

1, 3, 5, 15, 25, 75, 929, 2787, 4645, 13935, 23225

Step-4: Factors of 69680

List of positive integer factors of 69680 that divides 69675 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 40, 52, 65, 67, 80, 104, 130, 134, 208, 260, 268, 335, 520, 536, 670, 871, 1040, 1072, 1340, 1742, 2680, 3484, 4355, 5360, 6968, 8710, 13936, 17420, 34840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69675 and 69680. The biggest common factor number is the GCF number.
So the greatest common factor 69675 and 69680 is 5.

Also check out the Least Common Multiple of 69675 and 69680