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How many divisors of 10^5 end with a zero?
- a)1
- b)3
- c)9
- d)16
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
How many divisors of 10^5 end with a zero?a)1 b)3 c)9 d)16Correct answ...
For this, let's calculate the number of factors for 10^5
10^5 = 2^5 x 5^5
Total number of factors or divisors are (5+1) x (5+1) = 36
Factors ending with a single zero:
To end with a zero there should be only one pair of 2 x 5 (or 10) as part of the divisor.
So, let's take one 2 x 5 now there are 4 2’s and 4 5’s left for consideration.
We can select only 2’s in 4 ways and we can select only 5’s in 4 ways.
So, total = 4 + 4 + 1 ( 1 for just 2 x 5 ie 10) that is 9.
This question is part of UPSC exam. View all Quant courses
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How many divisors of 10^5 end with a zero?a)1 b)3 c)9 d)16Correct answ...
Community Answer
How many divisors of 10^5 end with a zero?a)1 b)3 c)9 d)16Correct answ...
All the options are wrong because the divisors are
10,20,40,50,80,100,160,200,250,400,500,800,1000,1250,2000,2500,5000,10000,20000,25000,50000,100000
10,20,40,50,80,100,160,200,250,400,500,800,1000,1250,2000,2500,5000,10000,20000,25000,50000,100000
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How many divisors of 10^5 end with a zero?a)1 b)3 c)9 d)16Correct answer is option 'C'. Can you explain this answer?
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