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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:How many factors of 24 × 35 × 104 are perfect squares which are greater than 1?

[2019]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:How many pairs (m, n) of positive integers satisfy the equation m2 + 105 = n2?

[2019]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of fifth and sixth digits. Then, the largest possible value of the fourth digit is?

[2019]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:If m and n are integers such that (√2)19 34 42 9m 8n = 3n 16m (∜64) then m is

[2019]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157 : 3, then the sum of the two numbers is

[2019]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:The number of integers x such that 0.25 < 2x < 200, and 2x + 2 is perfectly divisible by either 3 or 4, is

[2018]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:A sequence of 4 digits, when considered as a number in base 10 is four times the number it represents in base 6. What is the sum of the digits of the sequence?

[2016]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:Which of the following will completely divide (10690 – 4990)?

[2015]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:Let P be the set of all odd positive integers such that every element in P satisfies the following conditions.
I. 100 ≤ n < 1000
II. The digit at the hundred’s place is never greater than the digit at tens place and also never less than the digit at units place.

How many elements are there in P?

[2015]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:A four-digit number is divisible by the sum of its digits. Also, the sum of these four digits equals the product of the digits. What could be the product of the digits of such a number?

[2015]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:P is the product of the first 100 multiples of 15 and Q is the product of the first 50 multiples of 2520. Find the number of consecutive zeroes at the end of P2/Q × 101767 

[2015]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:The number of factors of the square of a natural number is 105. The number of factors of the cube of the same number is ‘F’. Find the maximum possible value of ‘F’.

[2013]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:‘ab’ is a two-digit prime number such that one of its digits is 3. If the absolute difference between the digits of the number is nota factor of 2, then how many values can ‘ab’ assume?

[2013]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:If E = 3 + 8 + 15 + 24 + … + 195, then what is the sum of the prime factors of E?

[2013]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:The number 44 is written as a product of 5 distinct integers. If ‘n’ is the sum of these five integers then what is the sum of all the possible values of n?

[2012]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:All the two-digit natural numbers whose unit digit is greater than their ten’s digit are selected. If all these numbers are written one after the other in a series, how many digits are there in the resulting number?

[2012]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:A positive integer is equal to the square of the number of factors it has. How many such integers are there?

[2011]

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Question for CAT Past Year Questions: Factors & Divisibility
Try yourself:If ‘a’ is one of the roots of x5 – 1 = 0 and a ≠ 1, then what is the value of a15 + a16 + a17 +.......a50?

[2010]

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FAQs on CAT Past Year Questions: Factors & Divisibility - Quantitative Aptitude (Quant)

1. What are factors and divisibility?
Factors are numbers that divide exactly into another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. Divisibility refers to the property of a number being divisible by another number without leaving a remainder. For example, 12 is divisible by 3 because 12 ÷ 3 = 4 with no remainder.
2. How do you find the factors of a given number?
To find the factors of a given number, you can divide the number by all possible smaller numbers and check if there is no remainder. Start with the number 1 and go up to the given number itself. The numbers for which the division is exact, without any remainder, are the factors of the given number.
3. What is the difference between factors and multiples?
Factors are the numbers that divide exactly into another number, while multiples are the numbers that a given number divides exactly into. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. The multiples of 3 are 3, 6, 9, 12, 15, and so on.
4. How can divisibility rules help in quickly determining if a number is divisible by another number?
Divisibility rules are helpful shortcuts or patterns that can be used to determine if a number is divisible by another number without actually performing the division. For example, the divisibility rule for 2 states that a number is divisible by 2 if its units digit is even. Similarly, the divisibility rule for 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3.
5. Can you provide an example of solving a divisibility problem using divisibility rules?
Sure! Let's say we want to determine if the number 486 is divisible by 9. According to the divisibility rule for 9, a number is divisible by 9 if the sum of its digits is divisible by 9. In this case, 4 + 8 + 6 = 18, which is divisible by 9. Therefore, we can conclude that 486 is divisible by 9.
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