What is the Greatest Common Factor of 78000 and 78020?

Greatest common factor (GCF) of 78000 and 78020 is 20.

GCF(78000,78020) = 20

We will now calculate the prime factors of 78000 and 78020, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 78000 and 78020.

How to find the GCF of 78000 and 78020?

We will first find the prime factorization of 78000 and 78020. After we will calculate the factors of 78000 and 78020 and find the biggest common factor number .

Step-1: Prime Factorization of 78000

Prime factors of 78000 are 2, 3, 5, 13. Prime factorization of 78000 in exponential form is:

78000 = 2⁴ × 3¹ × 5³ × 13¹

Step-2: Prime Factorization of 78020

Prime factors of 78020 are 2, 5, 47, 83. Prime factorization of 78020 in exponential form is:

78020 = 2² × 5¹ × 47¹ × 83¹

Step-3: Factors of 78000

List of positive integer factors of 78000 that divides 78000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 25, 26, 30, 39, 40, 48, 50, 52, 60, 65, 75, 78, 80, 100, 104, 120, 125, 130, 150, 156, 195, 200, 208, 240, 250, 260, 300, 312, 325, 375, 390, 400, 500, 520, 600, 624, 650, 750, 780, 975, 1000, 1040, 1200, 1300, 1500, 1560, 1625, 1950, 2000, 2600, 3000, 3120, 3250, 3900, 4875, 5200, 6000, 6500, 7800, 9750, 13000, 15600, 19500, 26000, 39000

Step-4: Factors of 78020

List of positive integer factors of 78020 that divides 78000 without a remainder.

1, 2, 4, 5, 10, 20, 47, 83, 94, 166, 188, 235, 332, 415, 470, 830, 940, 1660, 3901, 7802, 15604, 19505, 39010

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 78000 and 78020. The biggest common factor number is the GCF number.
So the greatest common factor 78000 and 78020 is 20.

Also check out the Least Common Multiple of 78000 and 78020