# CAT Practice : Number System: Factors

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The following topics are covered in the CAT quant section from Number system - HCF, LCM. Detailed explanatory answers, solution videos and slide decks are also provided.
1. ### Number Theory - Factors

The sum of the factors of a number is 124. What is the number?

1. Number lies between 40 and 50
2. Number lies between 50 and 60
3. Number lies between 60 and 80
4. More than one such number exists
More than one such number exists.
• Sum of factors
• Hard
2. ### Number Theory - Factors

How many factors of 1080 are perfect squares?

1. 4
2. 6
3. 8
4. 5
4
• Factors - Perfect Squares
• Medium
3. ### Number Theory - Factors

How many factors of 25 * 36 * 52 are perfect squares?

1. 18
2. 24
3. 36
4. 8
24
• Factors - Perfect Squares
• Medium
4. ### Number Theory - Odd Factors

How many factors of 24 * 53 * 74 are odd numbers?

1. 100
2. 99
3. 20
4. 24
5. ### Number Systems - Factors

How many factors of the number 28 * 36 * 54 * 105 are multiples of 120?

1. 540
2. 660
3. 594
4. 792
6. ### Number Theory - Even Factors

Number N = 26 * 55 * 76 * 107; how many factors of N are even numbers?

1. 1183
2. 1200
3. 1050
4. 840
1183
• Factors - Even numbers
• Medium
7. ### Number Theory - Perfect Cube

Numbers A, B, C and D have 16, 28, 30 and 27 factors. Which of these could be a perfect cube?

1. A and B
2. B and C
3. A, B and C
4. B and D
A and B
• Factors of perfect cube
• Medium
8. ### Number Theory 'abcabc'

If a three digit number ‘abc’ has 3 factors, how many factors does the 6-digit number ‘abcabc’ have?

1. 16 factors
2. 24 factors
3. 16 or 24 factors
4. 20 factors
16 or 24 factors
• Factors of a number abcabc
• Hard
9. ### Number Theory - Brute Force

How many numbers are there less than 100 that cannot be written as a multiple of a perfect square greater than 1?

1. 61
2. 56
3. 52
4. 65
10. ### Number Theory - 18 factors

Find the smallest number that has exactly 18 factors.

1. 180
2. 216
3. 240
4. None of these
180
• Smallest number with 18 factors
• Hard
11. ### Number Theory - Factors

A number N2 has 15 factors. How many factors can N have?

1. 5 or 7 factors
2. 6 or 8 factors
3. 4 or 6 factors
4. 9 or 8 factors
6 or 8 factors
• Number Theory - Factors
• Medium
12. ### Number Theory 'abcabc'

If a three digit number ‘abc’ has 2 factors (where a, b, c are digits), how many factors does the 6-digit number ‘abcabc’ have?

1. 16
2. 24
3. 18
4. 30
16
• Factors of a number abcabc
• Hard
13. ### 12 Factors

What is the smallest number that has exactly 12 factors ?

1. 211
2. 60
3. 120
4. 144

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