RRB Group D 17-Dec-2018 Shift 1 Soled Paper

Question : 67 of 100

Marks: +1, -0

Which is the smallest natural number having exactly 10 factors?

Solution:

No. of factor=

a^p×b^q=(P+1)×(q+1)

36=2×2×3×3=2^2×3^2

=(2+1)(2+1)=9

=(2+1)(2+1)=9

16=2×2×2×2=2^4=(4+1)=5

48=2×2×2×3=2^4×3^1

=(3+1)(1+)=8

or, Factors

36=1,2,3,4,6,9,12,18,36⇒9

16=1,2,4,8, 16⇒5

24= 1,2,3,4, 6,8,12,24 ⇒8

48 = 1,2,3,4,6,8,12,16,24,48⇒10

48 has 10 factors.

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