What is the Greatest Common Factor of 20750 and 20770?

Greatest common factor (GCF) of 20750 and 20770 is 10.

GCF(20750,20770) = 10

We will now calculate the prime factors of 20750 and 20770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20750 and 20770.

How to find the GCF of 20750 and 20770?

We will first find the prime factorization of 20750 and 20770. After we will calculate the factors of 20750 and 20770 and find the biggest common factor number .

Step-1: Prime Factorization of 20750

Prime factors of 20750 are 2, 5, 83. Prime factorization of 20750 in exponential form is:

20750 = 2¹ × 5³ × 83¹

Step-2: Prime Factorization of 20770

Prime factors of 20770 are 2, 5, 31, 67. Prime factorization of 20770 in exponential form is:

20770 = 2¹ × 5¹ × 31¹ × 67¹

Step-3: Factors of 20750

List of positive integer factors of 20750 that divides 20750 without a remainder.

1, 2, 5, 10, 25, 50, 83, 125, 166, 250, 415, 830, 2075, 4150, 10375

Step-4: Factors of 20770

List of positive integer factors of 20770 that divides 20750 without a remainder.

1, 2, 5, 10, 31, 62, 67, 134, 155, 310, 335, 670, 2077, 4154, 10385

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20750 and 20770. The biggest common factor number is the GCF number.
So the greatest common factor 20750 and 20770 is 10.

Also check out the Least Common Multiple of 20750 and 20770