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Number System: Basics of Factors Test-1

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Question 1
How many factors does 825 have
A
14
B
16
C
12
D
20
Question 1 Explanation: 
Step 1: Prime factorisation, so N=825= 31 52 111
Power of 3 as 3, 31 ( 1+1=2)ways ,
Power of 5 as 50 , 51 ,52  ( 2+1=3)ways
Power of 11 as 110, 111 (1+1=2)ways
Step 2: Hence, the number of factors is (1+1)(2+1)(1+1)=2x3x2=12
Question 2
How many are number of factors N= 32537311213217 ?
A
700
B
456
C
864
D
900
Question 2 Explanation: 
Step 1: Prime factorisation, so N=32537311213217 1
Power of 3 as 3, 31 ,32
Power of 5 as 50 , 51 ,52,53
Power of 7 as 70,71,72,73
Power of 11as 110111112
Power of 13 as 130131132
Power of 17 as 170171
Step 2:
Hence, the number of factors is(2+1)(3+1)(3+1)(2+1)(2+1)(1+1)=864
Question 3
How many even factors does the number 24 35 72 have?
A
76
B
72
C
36
D
128
Question 3 Explanation: 
In this case we have to find number of even factors,an even factor is divisible by 2 or smallest power of 2 has to be 1 not 0.
Hence a factor must be 2(1 or 2 or 3 or 4)3(0 or 1,2,3,4,5)7(0 or 1 or 2)
Hence total number of factors= (4)(5 + 1 )(2 + 1) = 72
Question 4
How many odd factors does the number N= 24 35 72?
A
20
B
40
C
45
D
18
Question 4 Explanation: 
To simply find odd factors, remove 2 from prime factors i.e from N remove ${{2}^{4}}$
Then we are left with $N={{3}^{5}}{{7}^{2}}$ Since these are two odd factors, they will have no even factors.
Therefore, the total number of factors is= (5+1)(2+1)=18
Question 5
How many factors are there in N = 25 5272 which are divisible by 10?
A
45
B
35
C
30
D
55
Question 5 Explanation: 
If a number is divisible by 10 then it must have minimum power of 2 and 5 as 1.
A factor divisible by 10 is 2(1 or 2 or 3or 4 or 5)5(1 or 2 )7(0 or 1 or 2 )
Hence, total number of factors divisible by 10 is = (5)(2)(2 + 1) = 30
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