GATE CS 2014 Set 2 — Question 59
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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Question
The number of distinct positive integral factors of 2014 is _________________________
Correct answer
8 to 8
Solution
To find the number of distinct positive integral factors, we first find the prime factorization of 2014. is even, so divide by 2:
Now we check 1007. It is not divisible by 3 (sum of digits is 8), not ending in 5.
Try dividing by 7: (No)
Try dividing by 11: (No)
Try dividing by 13: (No)
Try dividing by 17: (No)
Try dividing by 19: . (Yes)Both 19 and 53 are prime numbers.
So, the prime factorization is:
The number of factors is given by the product of one more than the exponents of the prime factors:
Number of factors .
Now we check 1007. It is not divisible by 3 (sum of digits is 8), not ending in 5.
Try dividing by 7: (No)
Try dividing by 11: (No)
Try dividing by 13: (No)
Try dividing by 17: (No)
Try dividing by 19: . (Yes)Both 19 and 53 are prime numbers.
So, the prime factorization is:
The number of factors is given by the product of one more than the exponents of the prime factors:
Number of factors .
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