What is the Greatest Common Factor of 53200 and 53210?

Greatest common factor (GCF) of 53200 and 53210 is 10.

GCF(53200,53210) = 10

We will now calculate the prime factors of 53200 and 53210, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53200 and 53210.

How to find the GCF of 53200 and 53210?

We will first find the prime factorization of 53200 and 53210. After we will calculate the factors of 53200 and 53210 and find the biggest common factor number .

Step-1: Prime Factorization of 53200

Prime factors of 53200 are 2, 5, 7, 19. Prime factorization of 53200 in exponential form is:

53200 = 2⁴ × 5² × 7¹ × 19¹

Step-2: Prime Factorization of 53210

Prime factors of 53210 are 2, 5, 17, 313. Prime factorization of 53210 in exponential form is:

53210 = 2¹ × 5¹ × 17¹ × 313¹

Step-3: Factors of 53200

List of positive integer factors of 53200 that divides 53200 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 19, 20, 25, 28, 35, 38, 40, 50, 56, 70, 76, 80, 95, 100, 112, 133, 140, 152, 175, 190, 200, 266, 280, 304, 350, 380, 400, 475, 532, 560, 665, 700, 760, 950, 1064, 1330, 1400, 1520, 1900, 2128, 2660, 2800, 3325, 3800, 5320, 6650, 7600, 10640, 13300, 26600

Step-4: Factors of 53210

List of positive integer factors of 53210 that divides 53200 without a remainder.

1, 2, 5, 10, 17, 34, 85, 170, 313, 626, 1565, 3130, 5321, 10642, 26605

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53200 and 53210. The biggest common factor number is the GCF number.
So the greatest common factor 53200 and 53210 is 10.

Also check out the Least Common Multiple of 53200 and 53210