Question

Match the following:

1.Total number of factors of 360	i) 78
2. Sum of all factors of 360	ii) 1092
3.Sum of all odd factors of 360	iii) 24
4.Sum of all even factors of 360	iv) 1170
5.Product of all factors of 360	v) ${360}^{12}$

• A. 1-v, 2-i, 3-iv, 4-iii, 5-ii
• B. 1-iii, 2-iv, 3-i, 4-ii, 5-v
• C. 1-ii, 2-v, 3-i, 4-iii, 5-iv
• D. 1-i, 2-iv, 3-iii, 4-ii, 5-v

Answer 1

The correct option is B 1-iii, 2-iv, 3-i, 4-ii, 5-v

We have,
$360=2^3\times 3^2\times 5$

a) Total number of factors
$=(3+1)\times (2+1)\times (1+1)$
$=4\times 3\times 2$
$=24$

b) Sum of all factors
$=(2^0+2^1+2^2+2^3)(3^0+3^1+3^2)(5^0+5^1)$
$=15\times 13\times 6$
$=1170$

c) Sum of all odd factors
$=(3^0+3^1+3^2)(5^0+5^1)$
$=13\times 6$
$=78$

d)Sum of all even factors
= Sum of all factors - sum of all odd factors
= 1170 -78
= 1092

e) Product of all factors
$={360}^{\frac{N}{2}}$ , where N is the total number of the factors

$={360}^{\frac{24}{2}}$

$={360}^{12}$