What is the Greatest Common Factor of 78400 and 78420?

Greatest common factor (GCF) of 78400 and 78420 is 20.

GCF(78400,78420) = 20

We will now calculate the prime factors of 78400 and 78420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78400 and 78420.

How to find the GCF of 78400 and 78420?

We will first find the prime factorization of 78400 and 78420. After we will calculate the factors of 78400 and 78420 and find the biggest common factor number .

Step-1: Prime Factorization of 78400

Prime factors of 78400 are 2, 5, 7. Prime factorization of 78400 in exponential form is:

78400 = 2⁶ × 5² × 7²

Step-2: Prime Factorization of 78420

Prime factors of 78420 are 2, 3, 5, 1307. Prime factorization of 78420 in exponential form is:

78420 = 2² × 3¹ × 5¹ × 1307¹

Step-3: Factors of 78400

List of positive integer factors of 78400 that divides 78400 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 32, 35, 40, 49, 50, 56, 64, 70, 80, 98, 100, 112, 140, 160, 175, 196, 200, 224, 245, 280, 320, 350, 392, 400, 448, 490, 560, 700, 784, 800, 980, 1120, 1225, 1400, 1568, 1600, 1960, 2240, 2450, 2800, 3136, 3920, 4900, 5600, 7840, 9800, 11200, 15680, 19600, 39200

Step-4: Factors of 78420

List of positive integer factors of 78420 that divides 78400 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 1307, 2614, 3921, 5228, 6535, 7842, 13070, 15684, 19605, 26140, 39210

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78400 and 78420. The biggest common factor number is the GCF number.
So the greatest common factor 78400 and 78420 is 20.

Also check out the Least Common Multiple of 78400 and 78420