What is the Greatest Common Factor of 32096 and 32100?

Greatest common factor (GCF) of 32096 and 32100 is 4.

GCF(32096,32100) = 4

We will now calculate the prime factors of 32096 and 32100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32096 and 32100.

How to find the GCF of 32096 and 32100?

We will first find the prime factorization of 32096 and 32100. After we will calculate the factors of 32096 and 32100 and find the biggest common factor number .

Step-1: Prime Factorization of 32096

Prime factors of 32096 are 2, 17, 59. Prime factorization of 32096 in exponential form is:

32096 = 2⁵ × 17¹ × 59¹

Step-2: Prime Factorization of 32100

Prime factors of 32100 are 2, 3, 5, 107. Prime factorization of 32100 in exponential form is:

32100 = 2² × 3¹ × 5² × 107¹

Step-3: Factors of 32096

List of positive integer factors of 32096 that divides 32096 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 59, 68, 118, 136, 236, 272, 472, 544, 944, 1003, 1888, 2006, 4012, 8024, 16048

Step-4: Factors of 32100

List of positive integer factors of 32100 that divides 32096 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 107, 150, 214, 300, 321, 428, 535, 642, 1070, 1284, 1605, 2140, 2675, 3210, 5350, 6420, 8025, 10700, 16050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32096 and 32100. The biggest common factor number is the GCF number.
So the greatest common factor 32096 and 32100 is 4.

Also check out the Least Common Multiple of 32096 and 32100