What is the Greatest Common Factor of 96105 and 96120?

Greatest common factor (GCF) of 96105 and 96120 is 15.

GCF(96105,96120) = 15

We will now calculate the prime factors of 96105 and 96120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 96105 and 96120.

How to find the GCF of 96105 and 96120?

We will first find the prime factorization of 96105 and 96120. After we will calculate the factors of 96105 and 96120 and find the biggest common factor number .

Step-1: Prime Factorization of 96105

Prime factors of 96105 are 3, 5, 43, 149. Prime factorization of 96105 in exponential form is:

96105 = 3¹ × 5¹ × 43¹ × 149¹

Step-2: Prime Factorization of 96120

Prime factors of 96120 are 2, 3, 5, 89. Prime factorization of 96120 in exponential form is:

96120 = 2³ × 3³ × 5¹ × 89¹

Step-3: Factors of 96105

List of positive integer factors of 96105 that divides 96105 without a remainder.

1, 3, 5, 15, 43, 129, 149, 215, 447, 645, 745, 2235, 6407, 19221, 32035

Step-4: Factors of 96120

List of positive integer factors of 96120 that divides 96105 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 89, 90, 108, 120, 135, 178, 180, 216, 267, 270, 356, 360, 445, 534, 540, 712, 801, 890, 1068, 1080, 1335, 1602, 1780, 2136, 2403, 2670, 3204, 3560, 4005, 4806, 5340, 6408, 8010, 9612, 10680, 12015, 16020, 19224, 24030, 32040, 48060

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 96105 and 96120. The biggest common factor number is the GCF number.
So the greatest common factor 96105 and 96120 is 15.

Also check out the Least Common Multiple of 96105 and 96120