Posted by **HELP HELP HELP MNHS** on Saturday, January 26, 2013 at 9:35pm.

How many positive factors does

62x(63^3+63^2+63+1)+1 have?

(with solution pls... thanks...)

- real number -
**Reiny**, Sunday, January 27, 2013 at 8:55am
63^3 + 63^2 + 63 + 1

= 63^2(63 + 1) + (63+1)

= (63^2 + 1)(63+1)

= 3970 x 64

62x(63^3+63^2+63+1)+1

= 62 x 3970 x 64 + 1

= 15752961

= 2401x6561

= 2401 x 3^8

= 7x343x3^8

= 7^4 x 3^8

So now we need to take different combinations of factors, e.g. 7x7 x 3x3x3 would be a factor

the four factors of 7 can be taken in 5 ways,

that is, take none, take one, take 2, take 3 or take 4 of them

in the same way, the eight 3's can be taken in 9 ways.

So the total number of subsets of the above is

5x9 or 45

BUT, that would include taking neither the 7 nor the 3

so we subtract 1

number of positive factors is 44

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