Question

Find the odd one among: 825, 645, 354, 312, 915, 715
A.715
B.915
C.312
D.354

Answer 1

Hint: First we will check for the multiplicity of 2 to find the odd one or we can say that the even and odd numbers, similarly we will check for the multiplicity of 3 and will keep checking until the we find the odd one out, we will find the multiplicity of numbers using the prime factorization method.

Complete step-by-step answer:
Given data: 825, 645, 354, 312, 915, 715
We will find the factors of the given number or we can say that we will write the given numbers using the prime factorization method.
 $825 = 3 \times {5^2} \times 11$
 $645 = 3 \times 5 \times 43$
 $354 = 2 \times 3 \times 59$
 $312 = {2^3} \times 3 \times 13$
 $915 = 3 \times 5 \times 61$
 $715 = 5 \times 11 \times 13$
Now first, we will check for the multiple of 2 or we can say that we will check the number of even and odd numbers,
There are two even and 4 odd numbers so we cannot find a single odd out based on a multiplicity of 2.
Now, check the multiples of 3,
We can see that there are 5 multiples of 3 and only one number i.e. 715 is not a multiple of 3.
Hence, Option (A) is correct.

Note: An alternative method can be
We know that for the multiplicity of 3 the sum of digits of the number should also be a multiple of 3
Sum of digits of the numbers
 $825 \to 8 + 2 + 5 = 15$
 $645 \to 6 + 4 + 5 = 15$
 $354 \to 3 + 5 + 4 = 12$
 $312 \to 3 + 1 + 2 = 6$
 $915 \to 9 + 1 + 5 = 15$
 $715 \to 7 + 1 + 5 = 13$
From the above results, we can say that 13 is the only number which is not a multiple of 3
Hence 715 is the odd one