Prime Factors

Q.

Using Euclid division algorithm find H.C.F of $867$ and $255$.

Q. Find the HCF and LCM of 90 and 144 by prime factorisation method.

1. 18 and 720
2. 720 and 18
3. 360 and 180
4. 180 and 720

Q.

Show that any positive odd integer is of the form $6\mathrm{q}+1$ or $6\mathrm{q}+2$ or $6\mathrm{q}+3$; where $\mathrm{q}$ is some integer.

Q.

Which number should be added to $195$ so that it becomes prime?

Q.

A number 'x' was found to be represented in the simplest $\frac{p}{q}$ form. The decimal expansion of this number was found to be 6.3333333333..... Find the value of p - q.

1. 13

2. 14

3. 12

4. 11

Q.

The number 0.42 in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$, is

1. 

2. 

3. 

4. 

Q. Explain why 371319+26 is a composite number.

Q.

Find the L.C.M of $112,140$ and $168$ using the common division method.

Q. What is the sum of LCM and HCF of 45, 75?

1. 215
2. 250
3. 225
4. 240

Q.

Complete the factor tree.

1. a = 2,
   b = 5,
   c = 5,
   d = 3 or 2,
   e = 2 or 3
2. a = 3,
   b = 2,
   c = 2,
   d = 5 or 2,
   e = 2 or 5

3. a = 2,
   b = 3,
   c = 3,
   d = 1or 10,
   e = 10 or 1

4. a = 3,
   b = 2,
   c = 3,
   d = 2 or 5,
   e = 5 or 2

Q.

Write all prime numbers between $40and80?$

Q.

(a) $\frac{22}{7}$ is a rational number but $\pi$ is an irrational number. Comment on this.

(b) Do the numbers $\frac{1}{3}$ and $\frac{-5}{2}$ lie on the opposite sides of 0 on the number line?

[3 MARKS]

Q.

The value of $x$ in, $3:5=15:x$ is ___.

Q.

Express $288$ as product of powers of their prime factors.

Q.

Complete the following factor trees and find the values of a, b, c, d, and e.

Q.

Write down the prime numbers between $90$ and $120$?

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Q.

The H.C.F and L.C.M of two numbers are $9$ and $270$ . If one of the number is $45$, find the other number.

Q.

Write down the prime numbers between $28$ and $44$?

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Q. Determine prime factorization of each of the following numbers:

(i) 216
(ii) 420
(iii) 468
(iv) 945
(v) 7325
(vi) 13915

Q.

The product of two numbers is$2625$. If the HCF of the numbers is $5$, find the LCM of the numbers.

Q. Express the following integers as a product of its prime factors:
(i) $420$ (ii) $468$ (iii) $945$ (iv) $7325$

Q. Express each of the following positive integers as the product of its prime factors:
$5005$

Q.

Anita saves $Rs4.65$ daily, find the least number of days she will save the exact number of rupees.

Q.

Write all prime numbers between 5 and 35

Q.

Question 98

In the following question, state whether the given statement is true (T) or false (F).
The LCM of two coprime numbers is equal to product of the numbers.

Q.

The value of $({{\left(2^2\right)}^2)}^2$ is:

1. 

2. 

3. 

4. 

Q. Determine the prime factors of 45470971

Q.

Good afternoon mam/sir

I am Harshita and my query is:

Find the least number which is exactly divisible by 14, 21, 24 and 42.

Thank you

Q.

Which is the smallest odd composite number? How many even prime numbers are there?

Q.

Question 1 (b)

Write all the factors of the given number:
15