Question

4. Number of divisors of n = 38808 (except 1 and n) is
a 74
b. 70
c. 68
d. 72​

Answer 1

$Given \: number \: n = 38808$

$Resolve \: n \: into \: product \:prime.$

2 | 38808

________

2 | 19404

________

2 | 9702

________

3 | 4851

________

3 | 1617

________

7 | 539

________

7 | 77

________

**** 11

$n = 388808 = 2^{3} \times 3^{2} \times 7^{2} \times 11^{1}$

$\blue {If \: n = p^{a}\times q^{b} \times r^{c} }$

$\orange {Where, p,q \: and \: r \: are \: prime \: numbers}$

$\pink { Number \: of \: divisors (n)}$

$\pink {= (a+1)(b+1)(c+1) }$

$Now, Number \: divisors \: of \: n \\= (3+1)(2+1)(2+1)(1+1) \\= 4 \times 3 \times 3 \times 2\\=72$

$Number \:of \:divisors ( Except \:1 \:and \: n)\\= 72 - 2 \\= 70$

Therefore.,

$Option \: \green { (b) } \:is \: correct.$

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