What are factors and prime factorization?

Answer 1

All numbers have factors. They are the building blocks of multiplication sentences. In the sentence 3 x 4 = 12, 3 and 4 are factors of 12.

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.

Answer 2

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

2, 3, 5 and 7 are prime factors of 210.

That's the prime factorization of 210.

Answer 3

All numbers have factors. They're the numbers that multiply to get the original number. 3 x 5 = 15. 3 and 5 are factors of 15. All composite numbers can be expressed as the product of prime numbers. This is accomplished by dividing the original number by prime numbers until all the factors are prime. A factor tree can help you visualize this.

Example: 30

30 Divide by two.

15,2 Divide by three.

5,3,2 Stop. All the factors are prime.

2 x 3 x 5 = 30

That's the prime factorization of 30.

Answer 4

Let us consider an integer x. If there is a smaller integer y, such x/y gives another integer: y is a factor of x. For example 5 is a factor of 10. If there is no y exists for a particular x, that x is a Prime number: 7 is prime.

Answer 5

A prime number is any integer which is greater than two and which can be divided evenly only by itself and 1. A factor of an integer is any number which will divide it evenly.