Question

Which of the following number has total 24 positive factors?

Answer 1

Step-by-step explanation:

2×2×2×3 is the answer

hope it will helps you

Answer 2

Q) Which of the following number has a total of 24 positive factors.

a) $21^{5} * 2^{3}$.

b) $2^{7} * 12^{3}$.

c) $2^{6} * 3^{4}$ .

d) 63 * 55.

Option(d) 63 × 55, number has total 24 positive factors.

Given,

4 numbers.

To Find,

Which number has a total of 24 positive factors?

Solution,

The first option is $21^{5} * 2^{3}$ can be written as by applying the prime factorization theorem,

$21^{5} * 2^{3}$ = $3^{5}* 7^{5} *2^{3}$

Then the total factors will be  6 × 6 × 4 = 144.

So, this is not equal to 24.

b) $2^{7} *12^{3}$ , it can be written as,

$2^{7} * (2^{2} * 3) ^{3}$ = $2^{14} *3^{3}$,

which is not equal to 24.

c) In option(c) the factors  $2^{6}* 3^{4}$ are 7 × 5,

but these factors are not equal to 24.

d) Option(d) i s 63 × 55,

$3^{2}$ × $5^{1}$ × $7^{1}$ × $11^{1}$ .

And the factors are = 3 × 2 × 2 × 2

That will be equal to  24.

Hence, the number 63 × 55, is the number that has a total of 24 positive factors.

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