Question

Write the prime factors of \[100\].

Answer 1

Hint: Prime numbers are numbers that are divisible only by \[1\] and itself. Factorise the given number by dividing it with the smallest possible prime number , obtain a quotient and then repeat the process by dividing the quotient till all the prime factors are obtained.

Complete step by step solution:
Factorization is the process in which a number is broken up into numbers which in turn can be multiplied to get the original number. A factor of a number is a number that divides the original number without leaving any remainder.
To find the prime factors of \[100\], first divide \[100\] by the lowest possible prime number. The least prime number is \[2\] and \[100\] is divisible by \[2\]. So divide \[100\] by \[2\]. The quotient is \[50\].
Again divide \[50\] by \[2\] as it is divisible by \[2\]. The quotient obtained is \[25\].
Next divide \[25\] by a prime number but \[25\] is not divisible by \[2\], so try the next prime number \[3\] again not possible, try the next prime number \[5\]. The quotient obtained now is \[5\].
Finally divide \[5\] by \[5\], now the quotient is \[1\] hence it can’t be divided further.
Hence the prime factors of \[100\] are \[1\], \[2\] and \[5\] and the prime factorization is written as:

\[100 = 1 \times 2 \times 2 \times 5 \times 5\].

Note:
In prime factorization, all the factors must be prime numbers. \[10,20,100\] are also factors of \[100\], but they must not be mentioned in this answer as they are not prime numbers. All factors can be obtained by multiplying the prime factors. All prime numbers also have two factors \[1\] and itself.