What is the Greatest Common Factor of 48144 and 48160?

Greatest common factor (GCF) of 48144 and 48160 is 16.

GCF(48144,48160) = 16

We will now calculate the prime factors of 48144 and 48160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48144 and 48160.

How to find the GCF of 48144 and 48160?

We will first find the prime factorization of 48144 and 48160. After we will calculate the factors of 48144 and 48160 and find the biggest common factor number .

Step-1: Prime Factorization of 48144

Prime factors of 48144 are 2, 3, 17, 59. Prime factorization of 48144 in exponential form is:

48144 = 2⁴ × 3¹ × 17¹ × 59¹

Step-2: Prime Factorization of 48160

Prime factors of 48160 are 2, 5, 7, 43. Prime factorization of 48160 in exponential form is:

48160 = 2⁵ × 5¹ × 7¹ × 43¹

Step-3: Factors of 48144

List of positive integer factors of 48144 that divides 48144 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 59, 68, 102, 118, 136, 177, 204, 236, 272, 354, 408, 472, 708, 816, 944, 1003, 1416, 2006, 2832, 3009, 4012, 6018, 8024, 12036, 16048, 24072

Step-4: Factors of 48160

List of positive integer factors of 48160 that divides 48144 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 43, 56, 70, 80, 86, 112, 140, 160, 172, 215, 224, 280, 301, 344, 430, 560, 602, 688, 860, 1120, 1204, 1376, 1505, 1720, 2408, 3010, 3440, 4816, 6020, 6880, 9632, 12040, 24080

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48144 and 48160. The biggest common factor number is the GCF number.
So the greatest common factor 48144 and 48160 is 16.

Also check out the Least Common Multiple of 48144 and 48160