What is the Greatest Common Factor of 35409 and 35420?

Greatest common factor (GCF) of 35409 and 35420 is 11.

GCF(35409,35420) = 11

We will now calculate the prime factors of 35409 and 35420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35409 and 35420.

How to find the GCF of 35409 and 35420?

We will first find the prime factorization of 35409 and 35420. After we will calculate the factors of 35409 and 35420 and find the biggest common factor number .

Step-1: Prime Factorization of 35409

Prime factors of 35409 are 3, 11, 29, 37. Prime factorization of 35409 in exponential form is:

35409 = 3¹ × 11¹ × 29¹ × 37¹

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 35409

List of positive integer factors of 35409 that divides 35409 without a remainder.

1, 3, 11, 29, 33, 37, 87, 111, 319, 407, 957, 1073, 1221, 3219, 11803

Step-4: Factors of 35420

List of positive integer factors of 35420 that divides 35409 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 35409 and 35420. The biggest common factor number is the GCF number.
So the greatest common factor 35409 and 35420 is 11.

Also check out the Least Common Multiple of 35409 and 35420