What is the Greatest Common Factor of 38080 and 38097?

Greatest common factor (GCF) of 38080 and 38097 is 17.

GCF(38080,38097) = 17

We will now calculate the prime factors of 38080 and 38097, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38080 and 38097.

How to find the GCF of 38080 and 38097?

We will first find the prime factorization of 38080 and 38097. After we will calculate the factors of 38080 and 38097 and find the biggest common factor number .

Step-1: Prime Factorization of 38080

Prime factors of 38080 are 2, 5, 7, 17. Prime factorization of 38080 in exponential form is:

38080 = 2⁶ × 5¹ × 7¹ × 17¹

Step-2: Prime Factorization of 38097

Prime factors of 38097 are 3, 17, 83. Prime factorization of 38097 in exponential form is:

38097 = 3³ × 17¹ × 83¹

Step-3: Factors of 38080

List of positive integer factors of 38080 that divides 38080 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 17, 20, 28, 32, 34, 35, 40, 56, 64, 68, 70, 80, 85, 112, 119, 136, 140, 160, 170, 224, 238, 272, 280, 320, 340, 448, 476, 544, 560, 595, 680, 952, 1088, 1120, 1190, 1360, 1904, 2240, 2380, 2720, 3808, 4760, 5440, 7616, 9520, 19040

Step-4: Factors of 38097

List of positive integer factors of 38097 that divides 38080 without a remainder.

1, 3, 9, 17, 27, 51, 83, 153, 249, 459, 747, 1411, 2241, 4233, 12699

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38080 and 38097. The biggest common factor number is the GCF number.
So the greatest common factor 38080 and 38097 is 17.

Also check out the Least Common Multiple of 38080 and 38097