# HCF

**LCM and HCF**

Factors and Multiples : All the numbers that divide a number completely, i.e., without leaving any remainder, are called factors of that number. For example, 24 is completely divisible by 1, 2, 3, 4, 6, 8, 12, 24. Each of these numbers is called a factor of 24 and 24 is called a multiple of each of these numbers … More on LCM and HCF

Question 1 |

Two numbers are in the ratio of 2:9. If their H. C. F. is 19, numbers are:

6, 27 | |

8, 36 | |

38, 171 | |

20, 90 |

**Arithmetic Aptitude 4**

**HCF**

**Ratio and Proportion**

**Discuss it**

Question 1 Explanation:

Let the numbers be 2X and 9X Then their H.C.F. is X, so X = 19 ∴ Numbers are (2x19 and 9x19) i.e. 38 and 171

Question 2 |

HCF of two numbers is 11 and their LCM is 385. If the numbers do not differ by more than 50, what is the sum of the two numbers ?

132 | |

35 | |

12 | |

36 |

**Numbers**

**LCM**

**HCF**

**Discuss it**

Question 2 Explanation:

Product of numbers = LCM x HCF = 11 x 385 = 4235
Let the numbers be of the form 11m and 11n, such that 'm' and 'n' are co-primes.
=> 11m x 11n = 4235
=> m x n = 35
=> (m,n) can be either of (1, 35), (35, 1), (5, 7), (7, 5).
=> The numbers can be (11, 385), (385, 11), (55, 77), (77, 55).
But it is given that the numbers cannot differ by more than 50.
Hence, the numbers are 55 and 77.
Therefore, sum of the two numbers = 55 + 77 = 132

Question 3 |

Two numbers are in the ratio of 5:7. If their LCM is 105, what is the difference between their squares ?

216 | |

210 | |

72 | |

840 |

**Numbers**

**LCM**

**HCF**

**Discuss it**

Question 3 Explanation:

Let 'h' be the HCF of the two numbers.
=> The numbers are 5h and 7h.
We know that Product of Numbers = LCM x HCF
=> 5h x 7h = 105 x h
=> h = 3
So, the numbers are 15 and 21.
Therefore, difference of their squares = 21

^{2}- 15^{2}= 441 - 225 = 216Question 4 |

Which is the largest number that divides 17, 23, 35, 59 to leave the same remainder in each case ?

2 | |

3 | |

6 | |

12 |

**Numbers**

**HCF**

**Discuss it**

Question 4 Explanation:

Required Number = HCF (23-17, 35-23, 59-35, 59-17)
Required Number = HCF (6, 12, 24, 42) = 6

Question 5 |

The LCM. of two numbers is 30 and their HCF. is 15. If one of the numbers is 30, then what is the other number?

30 | |

25 | |

15 | |

20 |

**LCM**

**HCF**

**Discuss it**

Question 5 Explanation:

Say another number =x
product of two numbers = product of HCF and LCM
x.30 = 15*30
x=15

Question 6 |

Express 252 as a product of primes.

2 * 2 * 3 * 3 * 7 | |

3* 3 * 3 * 3 * 7 | |

2 * 2 * 2* 3 * 7 | |

2 * 3 * 3 * 3 * 7 |

**HCF**

**Discuss it**

Question 7 |

Which of the following has the most number of divisors?

99 | |

101 | |

176 | |

182 |

**HCF**

**Discuss it**

Question 7 Explanation:

99 = 1 * 3 * 3 * 11
101 = 1 * 101
176 = 1 * 2 * 2 * 2 * 2 * 11
182 = 1 * 2 * 7 * 13
Clearly, 176 has the most number of divisors.

Question 8 |

A perfect number n is a number which is equal to the sum of its divisors. Which of the following is a perfect number?

6 | |

9 | |

15 | |

21 |

**HCF**

**Discuss it**

Question 8 Explanation:

6 is divisible by 1, 2 and 3. And, 6 = 1 + 2 + 3.

Question 10 |

Find the highest common factor of the following numbers:
4 * 27 * 3125
8 * 9 * 25 * 7
16 * 81 * 5 * 11 * 49

180 | |

360 | |

540 | |

1260 |

**HCF**

**Discuss it**

There are 15 questions to complete.