Determine-the-number-of-integral-factors-of-105840-excluding-1-and-105840-

Question Number 751 by 112358 last updated on 06/Mar/15

D e t e r m i n e t h e n u m b e r o f i n t e g r a l

f a c t o r s o f 105840, e x c l u d i n g 1

a n d 105840 .

Answered by prakash jain last updated on 06/Mar/15

105840 = 2 \times 5 \times 2 \times 5292 = 2^{2} \times 5 \times 2 \times 2646

= 2^{3} \times 5 \times 2 \times 1323 = 2^{4} \times 5 \times 3 \times 441

= 2^{4} \times 5 \times 3 \times 3 \times 147 = 2^{4} \times 5 \times 3^{2} \times 3 \times 49

= 2^{4} \times 3^{3} \times 5^{1} \times 7^{2}

Number of integral factors = (4 + 1) (3 + 1) (1 + 1) (2 + 1)

= 5 \times 4 \times 2 \times 3 = 180

Exclude 2 factors 1 and 105840

180 - 2 = 178