All composite numbers can be expressed as unique products of prime numbers. This is accomplished by dividing the original number and its factors by prime numbers until all the factors are prime. A factor tree can help you visualize this.
Example: 210
210 Divide by two.
105,2 Divide by three.
35,3,2 Divide by five.
7,5,3,2 Stop. All the factors are prime.
2 x 3 x 5 x 7 = 210
That's the prime factorization of 210.
As a product of its prime factors in exponents: 22*3*7 = 84
prime factors
ladder method
44 22,2 11,2,2
As a product of its prime factors: 3*5*31 = 465
As a product of its prime factors in exponents: 22*3*7 = 84
3 is a prime number. Prime numbers don't have factor trees. The factors of 3 are 1 and 3.
prime factors
ladder method
The prime factors of 20 using exponents is: 22x 5
44 22,2 11,2,2
As a product of its prime factors: 3*5*31 = 465
You do not necessarily need the common prime factors when finding the greatest common factor, but with large numbers or numbers for which you cannot easily determine all the factors, using prime factorization to determine the greatest common factor is the easiest method. The greatest common factor can then be determined by multiplying the common prime factors together. For example, when trying to find the greatest common factor of 2144 and 5672, finding all their possible factors to compare could be difficult. So, it is easier to find their prime factors, determine the prime factors they have in common, and then multiply the common prime factors to get the greatest common factor. For descriptions and examples of finding the greatest common factor, see the "Related Questions" links below.
5
The greatest common prime factor of 10 and 20 is 5.
2 x 25Combine the factors.2 x 2 x 5 = 20, the LCM
prime factors of 28 are: 2, 2, 7.prime factors of 75 are: 3, 5, 5.As 28 and 75 have no common prime factors, their greatest common factor is 1.