What is the Greatest Common Factor of 38075 and 38080?

Greatest common factor (GCF) of 38075 and 38080 is 5.

GCF(38075,38080) = 5

We will now calculate the prime factors of 38075 and 38080, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38075 and 38080.

How to find the GCF of 38075 and 38080?

We will first find the prime factorization of 38075 and 38080. After we will calculate the factors of 38075 and 38080 and find the biggest common factor number .

Step-1: Prime Factorization of 38075

Prime factors of 38075 are 5, 1523. Prime factorization of 38075 in exponential form is:

38075 = 5² × 1523¹

Step-2: 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-3: Factors of 38075

List of positive integer factors of 38075 that divides 38075 without a remainder.

1, 5, 25, 1523, 7615

Step-4: Factors of 38080

List of positive integer factors of 38080 that divides 38075 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38075 and 38080. The biggest common factor number is the GCF number.
So the greatest common factor 38075 and 38080 is 5.

Also check out the Least Common Multiple of 38075 and 38080