What is the Greatest Common Factor of 8380 and 8400?

Greatest common factor (GCF) of 8380 and 8400 is 20.

GCF(8380,8400) = 20

We will now calculate the prime factors of 8380 and 8400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8380 and 8400.

How to find the GCF of 8380 and 8400?

We will first find the prime factorization of 8380 and 8400. After we will calculate the factors of 8380 and 8400 and find the biggest common factor number .

Step-1: Prime Factorization of 8380

Prime factors of 8380 are 2, 5, 419. Prime factorization of 8380 in exponential form is:

8380 = 2² × 5¹ × 419¹

Step-2: Prime Factorization of 8400

Prime factors of 8400 are 2, 3, 5, 7. Prime factorization of 8400 in exponential form is:

8400 = 2⁴ × 3¹ × 5² × 7¹

Step-3: Factors of 8380

List of positive integer factors of 8380 that divides 8380 without a remainder.

1, 2, 4, 5, 10, 20, 419, 838, 1676, 2095, 4190

Step-4: Factors of 8400

List of positive integer factors of 8400 that divides 8380 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 140, 150, 168, 175, 200, 210, 240, 280, 300, 336, 350, 400, 420, 525, 560, 600, 700, 840, 1050, 1200, 1400, 1680, 2100, 2800, 4200

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8380 and 8400. The biggest common factor number is the GCF number.
So the greatest common factor 8380 and 8400 is 20.

Also check out the Least Common Multiple of 8380 and 8400