What is the prime factorization of 180?

Question

Jenny Bolton · Accepted Answer

Explanation:
The 180 factors, which are prime numbers, must be found.
A 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

Here are the first few prime numbers

2, 3, 5, 7, 11, 13, \dots .

A number which is not prime is a 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.

\Rightarrow 10 = 2 \times 5

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 \div 2 = 90

⋆ 90 \div 2 = 45 which cannot be divided by 2 \Rightarrow 3

⋆ 45 \div 3 = 15

⋆ 15 \div 3 = 5 which cannot be divided by 3 \Rightarrow 5

⋆ 5 \div 5 = 1

having reached 1, we are there

\Rightarrow 180 = 2 \times 2 \times 3 \times 3 \times 5 = 2^{2} \times 3^{2} \times 5

Orlando Paz · Accepted Answer

Damn, cool, I would not have solved this without your help, thanks dear, hugged

What is the prime factorization of 180?

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