What is the Greatest Common Factor of 75208 and 75225?

Greatest common factor (GCF) of 75208 and 75225 is 17.

GCF(75208,75225) = 17

We will now calculate the prime factors of 75208 and 75225, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75208 and 75225.

How to find the GCF of 75208 and 75225?

We will first find the prime factorization of 75208 and 75225. After we will calculate the factors of 75208 and 75225 and find the biggest common factor number .

Step-1: Prime Factorization of 75208

Prime factors of 75208 are 2, 7, 17, 79. Prime factorization of 75208 in exponential form is:

75208 = 2³ × 7¹ × 17¹ × 79¹

Step-2: Prime Factorization of 75225

Prime factors of 75225 are 3, 5, 17, 59. Prime factorization of 75225 in exponential form is:

75225 = 3¹ × 5² × 17¹ × 59¹

Step-3: Factors of 75208

List of positive integer factors of 75208 that divides 75208 without a remainder.

1, 2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 79, 119, 136, 158, 238, 316, 476, 553, 632, 952, 1106, 1343, 2212, 2686, 4424, 5372, 9401, 10744, 18802, 37604

Step-4: Factors of 75225

List of positive integer factors of 75225 that divides 75208 without a remainder.

1, 3, 5, 15, 17, 25, 51, 59, 75, 85, 177, 255, 295, 425, 885, 1003, 1275, 1475, 3009, 4425, 5015, 15045, 25075

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75208 and 75225. The biggest common factor number is the GCF number.
So the greatest common factor 75208 and 75225 is 17.

Also check out the Least Common Multiple of 75208 and 75225