What is the Greatest Common Factor of 75726 and 75740?

Greatest common factor (GCF) of 75726 and 75740 is 14.

GCF(75726,75740) = 14

We will now calculate the prime factors of 75726 and 75740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75726 and 75740.

How to find the GCF of 75726 and 75740?

We will first find the prime factorization of 75726 and 75740. After we will calculate the factors of 75726 and 75740 and find the biggest common factor number .

Step-1: Prime Factorization of 75726

Prime factors of 75726 are 2, 3, 7, 601. Prime factorization of 75726 in exponential form is:

75726 = 2¹ × 3² × 7¹ × 601¹

Step-2: Prime Factorization of 75740

Prime factors of 75740 are 2, 5, 7, 541. Prime factorization of 75740 in exponential form is:

75740 = 2² × 5¹ × 7¹ × 541¹

Step-3: Factors of 75726

List of positive integer factors of 75726 that divides 75726 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 601, 1202, 1803, 3606, 4207, 5409, 8414, 10818, 12621, 25242, 37863

Step-4: Factors of 75740

List of positive integer factors of 75740 that divides 75726 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140, 541, 1082, 2164, 2705, 3787, 5410, 7574, 10820, 15148, 18935, 37870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75726 and 75740. The biggest common factor number is the GCF number.
So the greatest common factor 75726 and 75740 is 14.

Also check out the Least Common Multiple of 75726 and 75740