Number of Factors/ 11
Number of Factors/
fgfgdf
Note:- Number of factor Power
N = 2a×3b×5c×7d ...........
Number of factors/ = (a+1)×(b+1)×(c+1)×(d+1)...........
Sum of factors/ =(2°+21+22+......+2a)×(3°+31+32+.....+3b)×(5°+51+52+....+5c)×(7°+71+72+...+7d)
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TYPE–1
1. Find the following value for the no. 100/
Concept :-
(a) Find the number of factors/
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(b) Find the number of even factors/
(c) Find the number of odd factors/
(d) Find the sum of all factors/
(e) Find the sum of all even factors/
(f) Find the sum of all odd factors/
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2. Find the following value of 240./
(a) Find the number of factor/
(b) Find the number of even factors/
(c) Find the sum of all factors/
(d) Find the sum of all factors/
(e) Find the sum of all even factors/
(f) Find the sum of all odd factors/
3. Find the following value of 360./
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= 1092
4. Find the following value of 1728./
5. Find the total numbers of odd factors of 420?/
(a) 15 (b) 16 (c) 17 (d) 8
6. Find the total numbers of odd factors of 3016 × 1618 × 2021?
3016 × 1618 × 2021
(a) 646 (b) 658 (c) 620 (d) 635
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TYPE–2
1. Fi nd t he number of fact ors of 240 which are mult i ple of 3./
(a) 11 (b) 11 (c) 9 (d) 12
2. Find the number of factors of 240 which are multiple of 4./
(a) 10 (b) 11 (c) 6 (d) 12
3. Find the number of factors of 240 which are multiple of 8./
(a) 10 (b) 8 (c) 9 (d) 12
4. Find the number of factors of 240 which are multiple of 5./
(a) 10 (b) 11 (c) 9 (d) 12
Concept :-
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5. Find the sum of all factors of 240 which are multiple of 5./
(a) 620 (b) 610 (c) 600 (c) 630
= 620
TYPE–3
1. How many factors of 240 which are perfect square?
(a) 1 (b) 2 (c) 3 (c) 4
2. How many factors of 240 which are perfect cube?/
(a) 1 (b) 2 (c) 3 (c) 4
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3. How many fact ors i n N whi ch are perfect cube? Where, N = 2 6 × 38 × 54
N N = 26 × 38 × 54
(a) 15 (b) 16 (c) 17 (c) 18
4. How many factors of N which are perfect square ? where, N = 215 × 37 × 73
N N = 215 × 37 × 73
(a) 64 (b) 65 (c) 62 (c) 60
5. If N = 29 × 37 × 54 × 73, then N is divisible by how many positive perfect squares
N = 29 × 37 × 54 × 73 N
(a) 120 (b) 140 (c) 144 (c) 100
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6. If N = 314 × 313 - 12 , then what is sthe largest prime factor of N?
N = 314 × 313 - 12 N
(a) 11 (b) 79 (c) 13 (c) 73
TYPE–4
Concept
1. The total numbers of 1 digit number which have only 3 factors of will be:
(a) 2 (b) 3 (c) 4 (c) 5
2. The total numbers of 2 digit number which have only 3 factors of will be:
(a) 3 (b) 2 (c) 5 (c) 4
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3. The total numbers of 3 digit number which have only 3 factors of will be:
(a) 6 (b) 7 (c) 8 (c) 5
4. The total numbers of 4 digit number which have only 3 factors of will be:
(a) 15 (b) 16 (c) 17 (c) 14
5. How many natural numbers upto 100 has odd numbers of factors?
(a) 10 (b) 11 (c) 9 (c) 12
6. How many natural numbers less than 160 has odd number of factors?
(a) 10 (b) 11 (c) 9 (c) 12
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7. How many natural numbers less than 300 has odd number of factors?/
(a) 15 (b) 16 (c) 17 (c) 18
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8. If the product of factors of which are at 7th and 9th from the starting result in the number N itself
then how many factors of N are there.
N N
(a) 15 (b) 16 (c) 17 (c) 18
9. If the product of factors of which are at 43th and 47th from the starting result in the number N
itself then how many factors of N are there-/
N N
(a) 88 (b) 89 (c) 90 (c) 91
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TYPE–5
1. If there are 16 factors of N between 1 and N then find tht total numbers of factors of N ?
N N N
(a) 30 (b) 32 (c) 33 (d) 35
2. If there are 26 factors of N between 1 and N then find tht total numbers of factors of N?
N N N
(a) 53 (b) 54 (c) 55 (d) 52
3. Find the average of all factors of 240?/
(a) 37 (b) 37.2 (c) 37.5 (d) 38
4. Find the product of all factors of 12./
(a) 1728 (b) 1518 (c) 1528 (d) 1718
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5. Find the product of all factors of 100./
(a) 107 (b) 108 (c) 109 (d) 1010
6. Find the product of all factors of 360./
(a) 36012 (b) 36013 (c) 36011 (d) 36010
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Concept
7. Find the number of factors of 360 that are perfect square as well perfect cube.
(a) 3 (b) 1 (c) 2 (d) 4
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8. Find the number of factors of 28 × 36 × 54 that are perfect as well as perfect cube.
28 × 36 × 54
(a) 4 (b) 5 (c) 6 (d) 8
9. Find the number of prime factors of 1613 × 124 × 158 × 73
1613 × 124 × 158 × 73
(a) 83 (b) 84 (c) 86 (d) 81
10. what is the maximum value of x that it will be exactly divisible?
1× 2× 3× 4 × 5× 6 × 7....×108
x
3x
(a) 51 (b) 52 (c) 53 (d) 54
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