What is the Greatest Common Factor of 13825 and 13832?

Greatest common factor (GCF) of 13825 and 13832 is 7.

GCF(13825,13832) = 7

We will now calculate the prime factors of 13825 and 13832, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13825 and 13832.

How to find the GCF of 13825 and 13832?

We will first find the prime factorization of 13825 and 13832. After we will calculate the factors of 13825 and 13832 and find the biggest common factor number .

Step-1: Prime Factorization of 13825

Prime factors of 13825 are 5, 7, 79. Prime factorization of 13825 in exponential form is:

13825 = 5² × 7¹ × 79¹

Step-2: Prime Factorization of 13832

Prime factors of 13832 are 2, 7, 13, 19. Prime factorization of 13832 in exponential form is:

13832 = 2³ × 7¹ × 13¹ × 19¹

Step-3: Factors of 13825

List of positive integer factors of 13825 that divides 13825 without a remainder.

1, 5, 7, 25, 35, 79, 175, 395, 553, 1975, 2765

Step-4: Factors of 13832

List of positive integer factors of 13832 that divides 13825 without a remainder.

1, 2, 4, 7, 8, 13, 14, 19, 26, 28, 38, 52, 56, 76, 91, 104, 133, 152, 182, 247, 266, 364, 494, 532, 728, 988, 1064, 1729, 1976, 3458, 6916

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13825 and 13832. The biggest common factor number is the GCF number.
So the greatest common factor 13825 and 13832 is 7.

Also check out the Least Common Multiple of 13825 and 13832