Question

What is the prime factorization of 45?

Answer 1

Hint: In this problem, we have to find the prime factors of the given number 45. We know that the given number 45 is a composite number and therefore it will have prime factors. We can now see how to calculate the prime factors of the given number. We can first divide the given number 45 with the smallest prime factor, 3. We can keep dividing until it gives a non-zero remainder and we can find the prime factors.

Complete step by step answer:
Here we have to find the prime factors of the given number 45.
We know that the given number 45 is a composite number and therefore it will have prime factors. We can now see how to calculate the prime factors of the given number.
We can first divide the given number 45 with the smallest prime factor, 3 (as we take 2, we will get fraction), we get
\[\Rightarrow 45\div 3=15\]
Here we will have 15 as quotient but we have the remainder as 0. So, we can divide 15 again to get a non-zero remainder.
\[\Rightarrow 15\div 3=5\]
 We cannot further divide the numbers as we divide 5 by 3, we will get a fraction.
The prime factors of 256 can be written as,
\[\Rightarrow {{5}^{1}}\times {{3}^{2}}\]
Therefore, the prime factors of 45 are \[5\times {{3}^{2}}\], where 5 and 3 are prime numbers.

Note: We should always remember that 45 has six factors, they are 1, 3, 5, 9, 15, 45 in which 5 and 3 are the prime factors. We should remember that prime factors are nothing but the number which are prime. We can also find the factors for the given number and take out the prime numbers which will be the prime factors.