Question

Prime factors of 143 are
(a). 2,11,13
(b). 11,13
(c). 2,3,7
(d). None

Answer 1

Hint: We have to use the factorization theorem which states that every composite number can be factored into a product of prime numbers.

Complete step-by-step answer:
To obtain the prime factors of 143, we have to factorize it with prime numbers till their product gives us 143.
To start the factorization, we note that a prime number will be a factor if it leaves a remainder of zero when the number is divided by it.
Now, when we divide 143 by 2, the remainder is 1. So, it is not a factor of 143.
When we divide 143 by 3, the remainder is 2. So, it is not a factor of 143.
When we divide 143 by 5, the remainder is 3. So, it is not a factor of 143.
When we divide 143 by 7, the remainder is 3. So, it is not a factor of 143.
when we divide 143 by 11, the remainder is 0. So, it is a factor of 143.
Now, once we get a factor, we have to divide the number by it and again start the factorization of the quotient till we get the quotient as a prime number.
when we divide 143 by 11, we get the quotient as 13 which is itself a prime number. Thus the factorization method is over and we obtain the factors of 143 as 11 and 13 and (b) is the correct option.

Note: It was asked to find the factors, 13 was a prime number and therefore the factorization was over in the second step. If we would have not got a prime number, we would have factorized the quotient again and its factors would also have been the factors of the original number i.e. 143.