# What are the ways to find the prime factors of a number?

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.

### What strategy do you use to find factors?

Assuming you want all factors of a number: 1) Split a number into prime factors. 2) Combine the prime factors in all possible ways. To get the prime factors, you can systematically try out dividing the number by prime numbers, up to the number's square root (once the square of the prime number you try out is greater than the original number, you need not continue). For example, to find out prime factors of numbers…

### What are some numbers that have an even number of factors?

One subset is prime numbers, since their factors are only 1 and the number itself. Other than that, there are many ways to end up with an even number of factors. The general equation for the number of factors is (p1+1)(p2+1) ... (p3 + 1) where the p values are the exponents of the prime factors of the number. So, as long as at least one prime factor is represented oddly (i.e., there is only…

### What is the greatest common factor of 8 and 49?

First, you must find the factors of each number. The factors of 49 are {1, 7, 49} because [1 x 49] and [7 x 7] are the only ways to make 49 using multiplication. The factors of 8 are {1, 2, 4, 8} because [1 x 8] and [2 x 4] are the only ways to make 8 using multiplication. The Greatest Common Factor is {1} because 1 is the only number included in both…

### What are the methods in finding a prime factorization?

There's really only one way to find a prime factorization; divide prime numbers into a given number and its factors until all the factors are prime. There are numerous ways to notate that process. A quick glance through this website reveals continuous division, quotients of 1, Euclidean method, division ladders and the various factor trees, fireworks, rainbows, etc.

### How do you find the prime factorization of a square root?

Two ways: Find the square root first. If it's a whole number, find the prime factorization like you would for any other number. Or, find the prime factorization of the original number. The factors will be paired. Take one out of of each pair. Example: 900 The square root of 900 is 30. The prime factorization of 30 is 2 x 3 x 5 or The prime factorization of 900 is 2 x 2 x…