What is the Greatest Common Factor of 54144 and 54162?

Greatest common factor (GCF) of 54144 and 54162 is 18.

GCF(54144,54162) = 18

We will now calculate the prime factors of 54144 and 54162, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 54144 and 54162.

How to find the GCF of 54144 and 54162?

We will first find the prime factorization of 54144 and 54162. After we will calculate the factors of 54144 and 54162 and find the biggest common factor number .

Step-1: Prime Factorization of 54144

Prime factors of 54144 are 2, 3, 47. Prime factorization of 54144 in exponential form is:

54144 = 2⁷ × 3² × 47¹

Step-2: Prime Factorization of 54162

Prime factors of 54162 are 2, 3, 17, 59. Prime factorization of 54162 in exponential form is:

54162 = 2¹ × 3³ × 17¹ × 59¹

Step-3: Factors of 54144

List of positive integer factors of 54144 that divides 54144 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 47, 48, 64, 72, 94, 96, 128, 141, 144, 188, 192, 282, 288, 376, 384, 423, 564, 576, 752, 846, 1128, 1152, 1504, 1692, 2256, 3008, 3384, 4512, 6016, 6768, 9024, 13536, 18048, 27072

Step-4: Factors of 54162

List of positive integer factors of 54162 that divides 54144 without a remainder.

1, 2, 3, 6, 9, 17, 18, 27, 34, 51, 54, 59, 102, 118, 153, 177, 306, 354, 459, 531, 918, 1003, 1062, 1593, 2006, 3009, 3186, 6018, 9027, 18054, 27081

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 54144 and 54162. The biggest common factor number is the GCF number.
So the greatest common factor 54144 and 54162 is 18.

Also check out the Least Common Multiple of 54144 and 54162