What is the Greatest Common Factor of 20825 and 20832?

Greatest common factor (GCF) of 20825 and 20832 is 7.

GCF(20825,20832) = 7

We will now calculate the prime factors of 20825 and 20832, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20825 and 20832.

How to find the GCF of 20825 and 20832?

We will first find the prime factorization of 20825 and 20832. After we will calculate the factors of 20825 and 20832 and find the biggest common factor number .

Step-1: Prime Factorization of 20825

Prime factors of 20825 are 5, 7, 17. Prime factorization of 20825 in exponential form is:

20825 = 5² × 7² × 17¹

Step-2: Prime Factorization of 20832

Prime factors of 20832 are 2, 3, 7, 31. Prime factorization of 20832 in exponential form is:

20832 = 2⁵ × 3¹ × 7¹ × 31¹

Step-3: Factors of 20825

List of positive integer factors of 20825 that divides 20825 without a remainder.

1, 5, 7, 17, 25, 35, 49, 85, 119, 175, 245, 425, 595, 833, 1225, 2975, 4165

Step-4: Factors of 20832

List of positive integer factors of 20832 that divides 20825 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 31, 32, 42, 48, 56, 62, 84, 93, 96, 112, 124, 168, 186, 217, 224, 248, 336, 372, 434, 496, 651, 672, 744, 868, 992, 1302, 1488, 1736, 2604, 2976, 3472, 5208, 6944, 10416

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20825 and 20832. The biggest common factor number is the GCF number.
So the greatest common factor 20825 and 20832 is 7.

Also check out the Least Common Multiple of 20825 and 20832