In how many ways can the number 18900 can be split into two factors which are relative prime (or co-prime).

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Concept- Find 18900's prime-factorization. So, calculate the total number of created prime numbers and use that amount as "n." Following are descriptions of how to split a single component into two relative prime components

2^{n - 1}

.
The reference number is 18900.
Relative prime or co-prime can be stated using integers, such as a and b.
If 1 is the sole positive integer that divides both of them, they are said to be coprime. For instance, the numbers 14 and 15 are co-prime and often only divide by 1. Because they are both divisible by 7, 14 and 21 are not coprime.
Prime factorization, which involves identifying the prime numbers that were multiplied together to create the original number, may now be used to divide the number 18900.

∴ 18900 = 2 \times 2 \times 3 \times 3 \times 3 \times 5 \times 5 \times 7

= (2 \times 2) \times (3 \times 3 \times 3) \times (5 \times 5) \times 7

= 2^{2} \times 3^{3} \times 5^{2} \times 7

Therefore, 18900's prime factorization is as follows:

18900 = 2^{2} \times 3^{3} \times 5^{2} \times 7

This suggests that there are actually four prime integers. The total number of co-prime integers is n, and in this case, n equals 4.
Therefore, the two relative prime ways that we can divide the number 18900 into two parts are