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Greatest common factor
Common factor of some numbers - a number, which is a factor of each of them. For example, numbers 36, 60, 42 have common factors 2 and 3 . Among all common factors there is always the greatest one, in our case this is 6. This number is called a greatest common factor (GCF).

To find a greatest common factor (GCF) of some numbers it is necessary:
  1. to express each of the numbers as a product of its prime factors, for example:
    360 = 2 · 2 · 2 · 3 · 3 · 5 ,
  2. to write powers of all prime factors in the factorization as:
    360 = 2 · 2 · 2 · 3 · 3 · 5 = 23 · 32 · 51 ,
  3. to write out all common factors in these factorizations;
  4. to take the least power of each of them, meeting in the all factorizations;
  5. to multiply these powers.
Example:
Find GCF for numbers: 168, 180 and 3024.
Solution:
168 = 2 · 2 · 2 · 3 · 7 = 23 · 31 · 71 ,
180 = 2 · 2 · 3 · 3 · 5 = 22 · 32 · 51 ,
3024 = 2 · 2 · 2 · 2 · 3 · 3 · 3 · 7 = 24 · 33 · 71 .
Write out the least powers of the common factors 2 and 3 and multiply them:
GCF = 22 · 31 = 12 .

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