What is the Greatest Common Factor of 75294 and 75309?

Greatest common factor (GCF) of 75294 and 75309 is 3.

GCF(75294,75309) = 3

We will now calculate the prime factors of 75294 and 75309, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75294 and 75309.

How to find the GCF of 75294 and 75309?

We will first find the prime factorization of 75294 and 75309. After we will calculate the factors of 75294 and 75309 and find the biggest common factor number .

Step-1: Prime Factorization of 75294

Prime factors of 75294 are 2, 3, 47, 89. Prime factorization of 75294 in exponential form is:

75294 = 2¹ × 3² × 47¹ × 89¹

Step-2: Prime Factorization of 75309

Prime factors of 75309 are 3, 13, 1931. Prime factorization of 75309 in exponential form is:

75309 = 3¹ × 13¹ × 1931¹

Step-3: Factors of 75294

List of positive integer factors of 75294 that divides 75294 without a remainder.

1, 2, 3, 6, 9, 18, 47, 89, 94, 141, 178, 267, 282, 423, 534, 801, 846, 1602, 4183, 8366, 12549, 25098, 37647

Step-4: Factors of 75309

List of positive integer factors of 75309 that divides 75294 without a remainder.

1, 3, 13, 39, 1931, 5793, 25103

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75294 and 75309. The biggest common factor number is the GCF number.
So the greatest common factor 75294 and 75309 is 3.

Also check out the Least Common Multiple of 75294 and 75309