Factors of a Number

Q. The H.C.F. and L.C.M. of two numbers are 12 and 924 respectively. Then the number of such pairs is ____.

1. 4
2. 2
3. 3
4. 0
5. 1

Q.

The least perfect square which is divisible by each of 21, 36 and 66, is?

1. 213444

2. 214344

3. 214434

4. 213429

5. 231444

Q.

A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is?

1. 9:5

2. 2:3

3. 4:7

4. 5:6

5. none

Q.

What is the smallest number by which 3600 be divided to make it a perfect cube?

1. 50

2. 9

3. 30

4. 450

5. 560

Q.

The smallest number added to 680621 to make the sum a perfect square is :

1. 4

2. 5

3. 8

4. 9

Q.

The least number by which 294 must be multiplied to make it a perfect square is?

1. 2

2. 3

3. 6

4. 24

5. 29

Q.

How to find number of divisors of a number.

Q.

Insert the missing number $2,8,5,6,8,?,11$

Q. 289, 361, 529, 841, 961, ?

1. 2209
2. 1681
3. 1369
4. 2136
5. 1849

Q.

The number of terms common to the A.P.’s $3,7,11,\dots 407$ and $2,9,16,\dots 709$ is

Q.

Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are5:3and1:2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio4:3. What is the ratio of the composition of the two basic elements in alloy X?

1. 1:1

2. 1:3

3. 1:4

4. none

Q.

A sum of Rs. 36.90 is made up of 180 coins which are either 10 paise coins or 25 p coins. The number of 10 p coins is:

1. 54

2. 45

3. 126

4. 154

5. none

Q.

Find the smallest number by which 5808 should be multiplied so that the product becomes a perfect square.

1. 2

2. 3

3. 11

4. 13

5. 7

Q.

The common factors of $17abc,34a{b}^2$ and $51a^{2}b$ is

1. $17abc$

2. $17ab$

3. $17ac$

4. $17a^2{b}^{2}c$

Q.

What is the least number which should be subtracted from 0.000326 to make it a perfect square?

1. 0.000002

2. 0.000004

3. 0.02

4. 0.04

5. 0.4

Q.

Using prime factorization, find which of the following are perfect squares.

$\left(a\right)484$

Q. x is the smallest number such that $\frac{x}{2}$ is a perfect square and is $\frac{x}{3}$ is a perfect cube. Then, the number of divisors of x is

1. 28
2. 12
3. 16
4. 24
5. 20

Q.

Fill in the missing number:
3, 6, 21, 28, 55, 66, ?, 120

1. None of the above
2. 106
3. 108
4. 105
5. 102

Q. $7^{6n}-6^{6n},$ where n is an integer $>0$, is divisible by (CAT 2002)

1. 559
2. All of these
3. 127
4. 13

Q. Find the number of factors of 240. Ans. _____________.

Q. 1331 2197 4913 6859 ? 24389

1. 12167
2. 13824
3. 9261
4. 15625
5. None of these

Q. In a coconut grove, (x + 2) trees yield 60 nuts per year, x trees yield 120 nuts per year, and (x - 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, find the value of x.

1. 4
2. 2
3. 8
4. 6
5. None of these

Q.

In a box, the ratio of Rs.1 coins, 50p coins and 25p coins can be expressed by three consecutive odd prime numbers that are in ascending order. The total value of coins in the box is Rs 58. If the number of Rs.1, 50p, 25p coins are reversed, find the new total value of coins in the box?

1. none

2. 72

3. 92

4. 82

5. 102

Q.

Which smallest number must be added to 2203 to get a perfect square?

1. 3

2. 5

3. 6

4. 4

Q. ${216}^{\frac{1}{3}}\times {26}^4\times {39}^4÷[{12}^4\times 3\times 2^{-36}]={13}^{?}$

1. 12
2. 4
3. 8
4. 10
5. 16

Q.

What is the prime factorization of $64$?

Q. Find the product of all prime numbers between 1 and 20

1. 9699670
2. 9699660
3. 9699645
4. 9699690
5. 9699680

Q.

Which is the smallest perfect square number that is divisible by 3, 4, 5, 6 and 8?

1. 900

2. 1200

3. 2500

4. 3600

5. 49000

Q.

The least positive integer $n$ for which ${}^{n-1}C_5+{}^{n-1}C_6<{}^{n}C_7$ is

1. $14$

2. $15$

3. $16$

4. $28$

Q.

The number of times the digits $3$ will be written when listing the integers from $1$ to $1000$ is?

1. $269$

2. $300$

3. $271$

4. $302$