What is the Greatest Common Factor of 35400 and 35420?

Greatest common factor (GCF) of 35400 and 35420 is 20.

GCF(35400,35420) = 20

We will now calculate the prime factors of 35400 and 35420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35400 and 35420.

How to find the GCF of 35400 and 35420?

We will first find the prime factorization of 35400 and 35420. After we will calculate the factors of 35400 and 35420 and find the biggest common factor number .

Step-1: Prime Factorization of 35400

Prime factors of 35400 are 2, 3, 5, 59. Prime factorization of 35400 in exponential form is:

35400 = 2³ × 3¹ × 5² × 59¹

Step-2: Prime Factorization of 35420

Prime factors of 35420 are 2, 5, 7, 11, 23. Prime factorization of 35420 in exponential form is:

35420 = 2² × 5¹ × 7¹ × 11¹ × 23¹

Step-3: Factors of 35400

List of positive integer factors of 35400 that divides 35400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 59, 60, 75, 100, 118, 120, 150, 177, 200, 236, 295, 300, 354, 472, 590, 600, 708, 885, 1180, 1416, 1475, 1770, 2360, 2950, 3540, 4425, 5900, 7080, 8850, 11800, 17700

Step-4: Factors of 35420

List of positive integer factors of 35420 that divides 35400 without a remainder.

1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 23, 28, 35, 44, 46, 55, 70, 77, 92, 110, 115, 140, 154, 161, 220, 230, 253, 308, 322, 385, 460, 506, 644, 770, 805, 1012, 1265, 1540, 1610, 1771, 2530, 3220, 3542, 5060, 7084, 8855, 17710

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35400 and 35420. The biggest common factor number is the GCF number.
So the greatest common factor 35400 and 35420 is 20.

Also check out the Least Common Multiple of 35400 and 35420