What is the Greatest Common Factor of 20400 and 20420?

Greatest common factor (GCF) of 20400 and 20420 is 20.

GCF(20400,20420) = 20

We will now calculate the prime factors of 20400 and 20420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20400 and 20420.

How to find the GCF of 20400 and 20420?

We will first find the prime factorization of 20400 and 20420. After we will calculate the factors of 20400 and 20420 and find the biggest common factor number .

Step-1: Prime Factorization of 20400

Prime factors of 20400 are 2, 3, 5, 17. Prime factorization of 20400 in exponential form is:

20400 = 2⁴ × 3¹ × 5² × 17¹

Step-2: Prime Factorization of 20420

Prime factors of 20420 are 2, 5, 1021. Prime factorization of 20420 in exponential form is:

20420 = 2² × 5¹ × 1021¹

Step-3: Factors of 20400

List of positive integer factors of 20400 that divides 20400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 25, 30, 34, 40, 48, 50, 51, 60, 68, 75, 80, 85, 100, 102, 120, 136, 150, 170, 200, 204, 240, 255, 272, 300, 340, 400, 408, 425, 510, 600, 680, 816, 850, 1020, 1200, 1275, 1360, 1700, 2040, 2550, 3400, 4080, 5100, 6800, 10200

Step-4: Factors of 20420

List of positive integer factors of 20420 that divides 20400 without a remainder.

1, 2, 4, 5, 10, 20, 1021, 2042, 4084, 5105, 10210

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20400 and 20420. The biggest common factor number is the GCF number.
So the greatest common factor 20400 and 20420 is 20.

Also check out the Least Common Multiple of 20400 and 20420