Question

How many different factors 48 have, excluding 1 and 48

Answer 1

Solution :

Resolving 48 into product of prime,

2 | 48
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2 | 24
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2 | 12
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2 | 6
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48 = 2³ × 3¹

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We know that ,

if m = p^a × q^b × r^c

where , p, q and r prime then

number of factors of m = (a+1)(b+1)(c+1)

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Now ,

number factors of 48 = (3 + 1 )(1 +1 )

= 4 × 2

= 8

Excluding two factors ( 1 and 48 )

number of different factors = 8 - 2

= 6

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