What is the Greatest Common Factor of 25725 and 25730?

Greatest common factor (GCF) of 25725 and 25730 is 5.

GCF(25725,25730) = 5

We will now calculate the prime factors of 25725 and 25730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25725 and 25730.

How to find the GCF of 25725 and 25730?

We will first find the prime factorization of 25725 and 25730. After we will calculate the factors of 25725 and 25730 and find the biggest common factor number .

Step-1: Prime Factorization of 25725

Prime factors of 25725 are 3, 5, 7. Prime factorization of 25725 in exponential form is:

25725 = 3¹ × 5² × 7³

Step-2: Prime Factorization of 25730

Prime factors of 25730 are 2, 5, 31, 83. Prime factorization of 25730 in exponential form is:

25730 = 2¹ × 5¹ × 31¹ × 83¹

Step-3: Factors of 25725

List of positive integer factors of 25725 that divides 25725 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 49, 75, 105, 147, 175, 245, 343, 525, 735, 1029, 1225, 1715, 3675, 5145, 8575

Step-4: Factors of 25730

List of positive integer factors of 25730 that divides 25725 without a remainder.

1, 2, 5, 10, 31, 62, 83, 155, 166, 310, 415, 830, 2573, 5146, 12865

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25725 and 25730. The biggest common factor number is the GCF number.
So the greatest common factor 25725 and 25730 is 5.

Also check out the Least Common Multiple of 25725 and 25730