# . What are the total number of divisors of 600(including 1 and 600)?

2
by keerti

2014-10-12T00:24:19+05:30

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There are a total of 24 divisors of 600 , including 1 and 600.
They are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300 and 600.
THANKU ANGELLA
You're welcome! :)
2014-10-12T09:14:16+05:30

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We can do this in some other ways other than listing the all factors.

1.  First find square root (600) = 24.5     There are always as many factors less
than square root as more than it.     The factors less than 24.5 are :

1,2,3,4,5,6,8,10,12,15,20,24.

there are 12 of them.   so above 24.5 ther are 12.
so total number of factors = 24

2. 600 = 2^3 * 3^1 * 5^2

A factor is formed by selecting one 2 or two 2s or three 2s or no 2s.  Also by      selecting no 3s or one 3.    finally,  no 5 may be chosen, 1 or two 5s may be      chosen to form a factor.

so number ways of forming a factor = 4 * 2 * 3 = 24

so 24 factors.

The first one is great thank you