What is the Greatest Common Factor of 36096 and 36105?

Greatest common factor (GCF) of 36096 and 36105 is 3.

GCF(36096,36105) = 3

We will now calculate the prime factors of 36096 and 36105, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36096 and 36105.

How to find the GCF of 36096 and 36105?

We will first find the prime factorization of 36096 and 36105. After we will calculate the factors of 36096 and 36105 and find the biggest common factor number .

Step-1: Prime Factorization of 36096

Prime factors of 36096 are 2, 3, 47. Prime factorization of 36096 in exponential form is:

36096 = 2⁸ × 3¹ × 47¹

Step-2: Prime Factorization of 36105

Prime factors of 36105 are 3, 5, 29, 83. Prime factorization of 36105 in exponential form is:

36105 = 3¹ × 5¹ × 29¹ × 83¹

Step-3: Factors of 36096

List of positive integer factors of 36096 that divides 36096 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 47, 48, 64, 94, 96, 128, 141, 188, 192, 256, 282, 376, 384, 564, 752, 768, 1128, 1504, 2256, 3008, 4512, 6016, 9024, 12032, 18048

Step-4: Factors of 36105

List of positive integer factors of 36105 that divides 36096 without a remainder.

1, 3, 5, 15, 29, 83, 87, 145, 249, 415, 435, 1245, 2407, 7221, 12035

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36096 and 36105. The biggest common factor number is the GCF number.
So the greatest common factor 36096 and 36105 is 3.

Also check out the Least Common Multiple of 36096 and 36105