What is the Greatest Common Factor of 35640 and 35649?

Greatest common factor (GCF) of 35640 and 35649 is 9.

GCF(35640,35649) = 9

We will now calculate the prime factors of 35640 and 35649, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35640 and 35649.

How to find the GCF of 35640 and 35649?

We will first find the prime factorization of 35640 and 35649. After we will calculate the factors of 35640 and 35649 and find the biggest common factor number .

Step-1: Prime Factorization of 35640

Prime factors of 35640 are 2, 3, 5, 11. Prime factorization of 35640 in exponential form is:

35640 = 2³ × 3⁴ × 5¹ × 11¹

Step-2: Prime Factorization of 35649

Prime factors of 35649 are 3, 17, 233. Prime factorization of 35649 in exponential form is:

35649 = 3² × 17¹ × 233¹

Step-3: Factors of 35640

List of positive integer factors of 35640 that divides 35640 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 18, 20, 22, 24, 27, 30, 33, 36, 40, 44, 45, 54, 55, 60, 66, 72, 81, 88, 90, 99, 108, 110, 120, 132, 135, 162, 165, 180, 198, 216, 220, 264, 270, 297, 324, 330, 360, 396, 405, 440, 495, 540, 594, 648, 660, 792, 810, 891, 990, 1080, 1188, 1320, 1485, 1620, 1782, 1980, 2376, 2970, 3240, 3564, 3960, 4455, 5940, 7128, 8910, 11880, 17820

Step-4: Factors of 35649

List of positive integer factors of 35649 that divides 35640 without a remainder.

1, 3, 9, 17, 51, 153, 233, 699, 2097, 3961, 11883

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35640 and 35649. The biggest common factor number is the GCF number.
So the greatest common factor 35640 and 35649 is 9.

Also check out the Least Common Multiple of 35640 and 35649