What is the Greatest Common Factor of 74725 and 74730?

Greatest common factor (GCF) of 74725 and 74730 is 5.

GCF(74725,74730) = 5

We will now calculate the prime factors of 74725 and 74730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74725 and 74730.

How to find the GCF of 74725 and 74730?

We will first find the prime factorization of 74725 and 74730. After we will calculate the factors of 74725 and 74730 and find the biggest common factor number .

Step-1: Prime Factorization of 74725

Prime factors of 74725 are 5, 7, 61. Prime factorization of 74725 in exponential form is:

74725 = 5² × 7² × 61¹

Step-2: Prime Factorization of 74730

Prime factors of 74730 are 2, 3, 5, 47, 53. Prime factorization of 74730 in exponential form is:

74730 = 2¹ × 3¹ × 5¹ × 47¹ × 53¹

Step-3: Factors of 74725

List of positive integer factors of 74725 that divides 74725 without a remainder.

1, 5, 7, 25, 35, 49, 61, 175, 245, 305, 427, 1225, 1525, 2135, 2989, 10675, 14945

Step-4: Factors of 74730

List of positive integer factors of 74730 that divides 74725 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 47, 53, 94, 106, 141, 159, 235, 265, 282, 318, 470, 530, 705, 795, 1410, 1590, 2491, 4982, 7473, 12455, 14946, 24910, 37365

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74725 and 74730. The biggest common factor number is the GCF number.
So the greatest common factor 74725 and 74730 is 5.

Also check out the Least Common Multiple of 74725 and 74730