HCF by Prime Factorization

Q.

Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. The sum of the digits in N is:

1. 5

2. 6

3. 7

4. 4

Q.

What is the greatest common factor of $12$ and $18$?

Q.

What is the greatest number by which $1037$ and $1159$ can both be divided exactly?

Q.

What can be the maximum value of HCF of any two numbers a and b given that a<b?

1. $\text{b}$

2. $\text{a}$

3. $\text{a}\times \text{b}$

4. $\frac{\text{a}}{\text{b}}$

Q. Jannat has 24 green beads and 30 orange beads. If the number of beads of the same colour in each bag have to be equal, then what is the maximum number of bags that can be packed?

1. 7
2. 6
3. 4
4. 5

Q. Question 4(ii)
Express each of the following as a product of prime factors only in exponential form:
(ii) 270

Q.

Find the H. C. F. of $30$and $42$ by prime factorization method.

Q.

What is the greatest common factor of $4$ and $10$?

Q. Find the H.C.F of 90 and 162.

1. 9
2. 18
3. 27
4. 3

Q. Three mugs contains 1401 mL, 1434 mL and 1464 mL of water respectively. Find the maximum capacity of the mug that can exactly measure the water of the three mugs?

1. 5 mL
2. 3 mL
   
3. 1 mL
   
4. 7 mL
   

Q.

What is the HCF of 15 and 120?

1. 25

2. 15

3. 11

4. 5

Q.

How do you find the greatest common factor ($\text{GCF}$) of two numbers?

Q.

Kate is stuck on the very first question of a maths test." Find the HCF of 15 and 30."
Help her by choosing the correct answer from the below choices.

1. 15

2. 5

3. 3

4. 10

Q.

Given that $(p+3)$ is the highest common factor of 81 and 108, find the value of $p$.

1. 12

2. 9

3. 24

4. 6

Q.

What is the H.C.F of 25 and 65?

1. 13

2. 3

3. 7

4. 5

Q. Choose the correct pairs.

1. $11$
2. Multiple of 13
3. $26$
4. Odd prime
5. 2
6. Even prime
7. HCF of 3 and 4
8. $1$
9. LCM of 12 and 24
10. $24$

Q. H.C.F of 45, 81 and 27 is _____.

1. 1

2. 45

3. 27

4. 9

Q.

The HCF of two consecutive odd numbers is:

1. 2

2. $1^{st}numberX{2}^{nd}number$

3. 1

4. None of these

Q.

What is the greatest number which divides 134 and 167 leaving 2 as the remainder in each case?

1. 34

2. 37

3. 39

4. 33

Q. 50 is the greatest common factor of 100 and 150.

1. True
2. False

Q. Compute the H.C.F of the pairs of numbers and sort the pairs in ascending order of their H.C.F.

1. 3, 5
2. 6, 8
3. 3, 9
4. 10, 15

Q.

What are the common multiples? If a number is divisible by 16, Which of the numbers will definitely be a factor of that number? [3 MARKS]