What is the prime factorization of 180?

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What is the prime factorization of 180?

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Answer 1 · 2016-08-11T12:54:22

$180 = 2^{2} \times 3^{2} \times 5$ $180=2^2xx3^2xx5$

Explanation:

We have to obtain the factors of 180 which are $prime numbers$ $color(blue)"prime numbers"$

A $prime number$ $color(blue)" prime number"$ being a number with only 2 factors.That is 1 and the number itself.

For example $5 only has 2 factors 1 and 5 \Rightarrow 5 = 1 \times 5$ $"5 only has 2 factors 1 and 5"rArr5=1xx5$

Here are the first few $prime numbers$ $color(blue)"prime numbers"$

$2,3,5,7,11,13,.....$

A number which is not prime is a $color(red)"composite number".$ Composite numbers have more than 2 factors. All composite numbers can be expressed as a product of prime factors.

For example 10 has factors 1 ,2 ,5 and 10 but can be expressed as a product of prime factors.

$rArr10=2xx5$

There are a variety of ways to find the prime factors of a number. Here is one.

Starting with 180, divide it by the lowest prime number 2 , repeat until it cannot be divided by 2 and move on to next prime number 3 and so on. When the remainder is 1 stop-we have obtained our prime factors.

$•180÷color(red)(2)=90$

$•90÷color(red)(2)=45 " which cannot be divided by" 2to3$

$•45÷color(red)(3)=15$

$•15÷color(red)(3)=5" which cannot be divided by" 3to5$

$•5÷color(red)(5)=1" having reached 1, we are there"$

$rArr180=color(red)(2xx2xx3xx3xx5)=2^2xx3^2xx5$

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What is the prime factorization of 180?

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