What is the Greatest Common Factor of 6825 and 6832?

Greatest common factor (GCF) of 6825 and 6832 is 7.

GCF(6825,6832) = 7

We will now calculate the prime factors of 6825 and 6832, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6825 and 6832.

How to find the GCF of 6825 and 6832?

We will first find the prime factorization of 6825 and 6832. After we will calculate the factors of 6825 and 6832 and find the biggest common factor number .

Step-1: Prime Factorization of 6825

Prime factors of 6825 are 3, 5, 7, 13. Prime factorization of 6825 in exponential form is:

6825 = 3¹ × 5² × 7¹ × 13¹

Step-2: Prime Factorization of 6832

Prime factors of 6832 are 2, 7, 61. Prime factorization of 6832 in exponential form is:

6832 = 2⁴ × 7¹ × 61¹

Step-3: Factors of 6825

List of positive integer factors of 6825 that divides 6825 without a remainder.

1, 3, 5, 7, 13, 15, 21, 25, 35, 39, 65, 75, 91, 105, 175, 195, 273, 325, 455, 525, 975, 1365, 2275

Step-4: Factors of 6832

List of positive integer factors of 6832 that divides 6825 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 61, 112, 122, 244, 427, 488, 854, 976, 1708, 3416

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6825 and 6832. The biggest common factor number is the GCF number.
So the greatest common factor 6825 and 6832 is 7.

Also check out the Least Common Multiple of 6825 and 6832