CAT Factors, divisibility, HCF & LCM Questions

Factor and divisibility problems describe how integers are built from primes. HCF takes shared prime powers, while LCM takes the powers needed to include every given integer.

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Key concepts

Prime factorisation and divisor counts
Divisibility rules
HCF and LCM

CAT factors, divisibility, hcf & lcm practice questions

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Practise Free Tests on InsideIIM

Common mistakes

Treating one as a prime number.
Applying HCF × LCM = product to more than two numbers without justification.

Practical solving approaches

Write prime factorizations and compare exponents.
Separate conditions on common factors from conditions on common multiples.

Factors, divisibility, HCF & LCM FAQs

How do I find HCF and LCM from prime factors?: Use the minimum exponent of each prime for HCF and the maximum exponent for LCM, treating an absent prime as exponent zero.

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CAT factors, divisibility, hcf & lcm practice questions

Question 1Type in the answerMEDIUM

Type in your answer in the input box provided below the question.

Answer the questions independently of each other.

Five bells begin to toll together and toll respectively at intervals of 6, 7, 8, 9 and 12 seconds. How many times they will toll together in one hour?

Question 2Type in the answerMEDIUM

Type in your answer in the input box provided below the question.

Answer the questions independently of each other.

An architect has to measure lengths of 625 cm, 1090 cm and 2000 cm. What should be the length of the tape so that he is able to perform the job in minimum number of integral steps?

Question 3Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Each question is followed by two statements, I and II.

Mark [1], if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.

Mark [2], if the question can be answered by using either statement alone.

Mark [3], if the question can be answered using both statements together, but cannot be answered using either statement alone.

Mark [4], if the question cannot be answered even by using both statements together.

Is y a perfect square, where x and y are natural numbers?

I. y is divisible by (x + 1) and (x + 2).

II. y < 200

Question 4Multiple choiceHARD

Select the correct alternative from the given choices.

Answer the questions independently of each other.

How many numbers are there between 1 and 30 including both the numbers such that n! is divisible by (n + 1)?

Question 5Multiple choiceEASY

Select the correct alternative from the given choices.

Answer the questions independently of each other.

n being any odd number greater than 1, n⁶⁵ – n is always divisible by:

Question 6Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Ram visits the Recreation club every 5 days, Harish visits every 24 days, while Rajesh goes there after every 9 days. If all three of them met at the club last time on a Sunday on what day of the week will all three meet again?

Question 7Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Answer the questions independently of each other.

How many even integers n, where 100 < n < 200, are divisible neither by seven nor by nine?

Question 8Multiple choiceHARD

Select the correct alternative from the given choices.

Answer the questions independently of each other.

The number of positive integers n in the range 12 < n < 40 such that the product (n – 1)(n – 2) ... 3.2.1 is not divisible by n is:

Question 9Type in the answerMEDIUM

Type in your answer in the input box provided below the question.

Answer the questions independently of each other.

There is a bell game in a casino at Mumbai. In a bell game there are five bells which toll at intervals of 12 sec, 5 sec, 7 sec, 8 sec and 10 sec respectively. Whenever all the five bells rings together, a person wins Rs.100. How much can a person win if he plays that game for 1 hr? (Note that initially all the bells ring together, but it is not counted as a win).

Question 10Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Answer the questions independently of each other.

A certain number N can be expressed as a product of two distinct numbers in '11' ways. The least possible value for N is:

Question 11Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Consider the set S = {1, 2, 3, …, 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?

CAT Factors, divisibility, HCF & LCM Questions

Factor and divisibility problems describe how integers are built from primes. HCF takes shared prime powers, while LCM takes the powers needed to include every given integer.

Loading question count…

Key concepts

Prime factorisation and divisor counts
Divisibility rules
HCF and LCM

CAT factors, divisibility, hcf & lcm practice questions

Loading questions…

Practise Free Tests on InsideIIM

Common mistakes

Treating one as a prime number.
Applying HCF × LCM = product to more than two numbers without justification.

Practical solving approaches

Write prime factorizations and compare exponents.
Separate conditions on common factors from conditions on common multiples.

Factors, divisibility, HCF & LCM FAQs

How do I find HCF and LCM from prime factors?: Use the minimum exponent of each prime for HCF and the maximum exponent for LCM, treating an absent prime as exponent zero.

Loading practice data…

CAT factors, divisibility, hcf & lcm practice questions

Question 1Type in the answerMEDIUM

Type in your answer in the input box provided below the question.

Answer the questions independently of each other.

Five bells begin to toll together and toll respectively at intervals of 6, 7, 8, 9 and 12 seconds. How many times they will toll together in one hour?

Question 2Type in the answerMEDIUM

Type in your answer in the input box provided below the question.

Answer the questions independently of each other.

An architect has to measure lengths of 625 cm, 1090 cm and 2000 cm. What should be the length of the tape so that he is able to perform the job in minimum number of integral steps?

Question 3Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Question 4Multiple choiceHARD

Select the correct alternative from the given choices.

Answer the questions independently of each other.

How many numbers are there between 1 and 30 including both the numbers such that n! is divisible by (n + 1)?

Question 5Multiple choiceEASY

Select the correct alternative from the given choices.

Answer the questions independently of each other.

n being any odd number greater than 1, n⁶⁵ – n is always divisible by:

Question 6Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Question 7Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Answer the questions independently of each other.

How many even integers n, where 100 < n < 200, are divisible neither by seven nor by nine?

Question 8Multiple choiceHARD

Select the correct alternative from the given choices.

Answer the questions independently of each other.

The number of positive integers n in the range 12 < n < 40 such that the product (n – 1)(n – 2) ... 3.2.1 is not divisible by n is:

Question 9Type in the answerMEDIUM

Type in your answer in the input box provided below the question.

Answer the questions independently of each other.

Question 10Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Answer the questions independently of each other.

A certain number N can be expressed as a product of two distinct numbers in '11' ways. The least possible value for N is:

Question 11Multiple choiceMEDIUM

Select the correct alternative from the given choices.

Consider the set S = {1, 2, 3, …, 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?

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CAT Factors, divisibility, HCF & LCM Questions

Key concepts

CAT factors, divisibility, hcf & lcm practice questions

Common mistakes

Practical solving approaches

Factors, divisibility, HCF & LCM FAQs

CAT Factors, divisibility, HCF & LCM Questions

Key concepts

CAT factors, divisibility, hcf & lcm practice questions

Common mistakes

Practical solving approaches

Factors, divisibility, HCF & LCM FAQs

More Number Systems practice

CAT Factors, divisibility, HCF & LCM Questions

Key concepts

CAT factors, divisibility, hcf & lcm practice questions

Common mistakes

Practical solving approaches

Factors, divisibility, HCF & LCM FAQs

CAT Factors, divisibility, HCF & LCM Questions

Key concepts

CAT factors, divisibility, hcf & lcm practice questions

Common mistakes

Practical solving approaches

Factors, divisibility, HCF & LCM FAQs

More Number Systems practice