What is the greatest common factor of 372 and 510?

the greatest common factor between 372 and 510 is 6
Two methods I can suggest:

• Find the prime factors of each number, collate and multiply together the common prime factors:

372 = 2 x 2 x 3 x 31

510 = 2 x 3 x 5 x 17

common prime factors = 2, 3

Greatest Common Factor = 2 x 3 = 6

To collate the common prime factors, it is often easier to mark each pair found (for example lightly crossing off or underlining)

In collating the common factors, every time a pair appears the factor is noted; for example CGF of 36 and 48:

36 = 2 x 2 x 3 x 3

48 = 2 x 2 x 2 x 2 x 3

common prime factors = 2, 2, 3

GCF = 2 x 2 x 3 = 12

• Euclid's method:
  1. Divide the larger by the smaller
  2. Ignoring the quotient, look at the remainder
  3. If remainder is zero, the divisor (smaller of the two numbers) is the GCF
  4. Otherwise, repeat steps 1-3 with the divisor (smaller number) and the remainder

510 / 372 = 1 r 138

372 / 138 = 2 r 96

138 / 96 = 1 r 42

96 / 42 = 2 r 12

42 / 12 = 3 r 6

12 / 6 = 2 r 0

GCF = 6