What is the Greatest Common Factor of 48146 and 48160?

Greatest common factor (GCF) of 48146 and 48160 is 14.

GCF(48146,48160) = 14

We will now calculate the prime factors of 48146 and 48160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48146 and 48160.

How to find the GCF of 48146 and 48160?

We will first find the prime factorization of 48146 and 48160. After we will calculate the factors of 48146 and 48160 and find the biggest common factor number .

Step-1: Prime Factorization of 48146

Prime factors of 48146 are 2, 7, 19, 181. Prime factorization of 48146 in exponential form is:

48146 = 2¹ × 7¹ × 19¹ × 181¹

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 48146

List of positive integer factors of 48146 that divides 48146 without a remainder.

1, 2, 7, 14, 19, 38, 133, 181, 266, 362, 1267, 2534, 3439, 6878, 24073

Step-4: Factors of 48160

List of positive integer factors of 48160 that divides 48146 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 48146 and 48160. The biggest common factor number is the GCF number.
So the greatest common factor 48146 and 48160 is 14.

Also check out the Least Common Multiple of 48146 and 48160