What is the Greatest Common Factor of 96120 and 96138?

Greatest common factor (GCF) of 96120 and 96138 is 18.

GCF(96120,96138) = 18

We will now calculate the prime factors of 96120 and 96138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 96120 and 96138.

How to find the GCF of 96120 and 96138?

We will first find the prime factorization of 96120 and 96138. After we will calculate the factors of 96120 and 96138 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 96138

Prime factors of 96138 are 2, 3, 7, 109. Prime factorization of 96138 in exponential form is:

96138 = 2¹ × 3² × 7² × 109¹

Step-3: Factors of 96120

List of positive integer factors of 96120 that divides 96120 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

Step-4: Factors of 96138

List of positive integer factors of 96138 that divides 96120 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 109, 126, 147, 218, 294, 327, 441, 654, 763, 882, 981, 1526, 1962, 2289, 4578, 5341, 6867, 10682, 13734, 16023, 32046, 48069

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 96120 and 96138. The biggest common factor number is the GCF number.
So the greatest common factor 96120 and 96138 is 18.

Also check out the Least Common Multiple of 96120 and 96138