What is the Greatest Common Factor of 32025 and 32032?

Greatest common factor (GCF) of 32025 and 32032 is 7.

GCF(32025,32032) = 7

We will now calculate the prime factors of 32025 and 32032, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32025 and 32032.

How to find the GCF of 32025 and 32032?

We will first find the prime factorization of 32025 and 32032. After we will calculate the factors of 32025 and 32032 and find the biggest common factor number .

Step-1: Prime Factorization of 32025

Prime factors of 32025 are 3, 5, 7, 61. Prime factorization of 32025 in exponential form is:

32025 = 3¹ × 5² × 7¹ × 61¹

Step-2: Prime Factorization of 32032

Prime factors of 32032 are 2, 7, 11, 13. Prime factorization of 32032 in exponential form is:

32032 = 2⁵ × 7¹ × 11¹ × 13¹

Step-3: Factors of 32025

List of positive integer factors of 32025 that divides 32025 without a remainder.

1, 3, 5, 7, 15, 21, 25, 35, 61, 75, 105, 175, 183, 305, 427, 525, 915, 1281, 1525, 2135, 4575, 6405, 10675

Step-4: Factors of 32032

List of positive integer factors of 32032 that divides 32025 without a remainder.

1, 2, 4, 7, 8, 11, 13, 14, 16, 22, 26, 28, 32, 44, 52, 56, 77, 88, 91, 104, 112, 143, 154, 176, 182, 208, 224, 286, 308, 352, 364, 416, 572, 616, 728, 1001, 1144, 1232, 1456, 2002, 2288, 2464, 2912, 4004, 4576, 8008, 16016

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32025 and 32032. The biggest common factor number is the GCF number.
So the greatest common factor 32025 and 32032 is 7.

Also check out the Least Common Multiple of 32025 and 32032