Question

What are the prime factors of 225.

Answer 1

Hint: Now we know that the prime factors are nothing but the factors which are prime numbers. Now we will first find the first prime factor by using divisibility test and then divide the number by it. Now we will again divide the obtained quotient and hence continue the process till we get all the prime factors.

Complete step by step solution:
Now first let us understand the concept of factors.
Factors of a number are all the numbers which can divide the given number. Now let us understand this by an example. Consider the number 10. We know that 10 can be divided by 1, 2, 5 and 10. Hence the numbers 1, 2, 5 and 10 are factors of 10.
Now let us understand prime numbers.
Prime numbers are numbers which have only 2 factors 1 and itself. Hence no other number will perfectly divide a prime number. For example 3, 7, 5
Now consider the given number 225.
Here we have the sum of digits as 2 + 2 + 5 = 9.
Since the sum of digits is divisible by 3 we can say by divisibility test of 3 that the number is divisible by 3.
Hence 3 is a factor of the number 225.
Hence we get $225=3\times 75$
Now here 3 is a prime number. Let us consider 75.
Here we have 7 + 5 = 12 which is again divisible by 3.
Hence we get 75 is also divisible by 3. Now we get $75=3\times 25$
Hence we get $225=3\times 3\times 25$
Now consider 25.
We know that 25 is nothing but square of 5. Hence we can write 25 as $5\times 5$ .
Hence we get factorization of 225 as $225=3\times 3\times 5\times 5$ .
Since all the factors in the above equation are prime we can say the prime factors of 225 are 3, 3, 5 and 5.

Note: Now note that if the number is prime it will have just 2 prime factors 1 and the number itself. Also note that every number has unique prime factorization. We can also find the square root and cube root of the number by expressing the number as multiple of its prime factors.