# Prime Factorisation

## Trending Questions

**Q.**

Prove that for any positive integer $n,{n}^{3}-n$ is divisible by $6$.

**Q.**

Express 5005 as a product of its prime factors.

**Q.**

If 3 is is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of a+b , is

**Q.**a and b are two positive integers such that the least prime factor of a is 3 and and that of b is 5.find the least prime factor of (a+b).

**Q.**

Find the simplest form of :

(i) 6992 (ii) 473645 (iii) 10951168 (iv) 368496

**Q.**

Whether $8$power $n$ , where $n$ is a natural number, can end with zero?

**Q.**

Express 140 as the product of its prime factors:

**Q.**

Determine the prime factorisation of each of the following positive integer:

(i) 20570 (ii) 58500 (iii) 45470971

**Q.**

Which of the following are the prime factors of 5005?

2

3

4

5

**Q.**

Express each of the following integers as a product of its prime factors:

(i) 420 (ii) 468 (iii) 945 (iv) 7325

**Q.**

Express 360 as product of its prime factors.

**Q.**

Question 1 (ii)

Express 156 as the product of its prime factors.

**Q.**The number of prime factors of 36 is:

- 2
- 3
- 4
- 6

**Q.**What is the total number of factors of a prime number?

**Q.**The sum of two prime number is always a prime number (True/ False).

**Q.**

How many prime factors are there in prime factorisation of 5005?

7

6

2

4

**Q.**Express 23150 as product of its prime factors. Is it unique?

**Q.**

A boy with a collection of marble realise that if he makes a group of 5 or 6 marbles at a time there are always 2 marbles left. Can you explain why the boy cannot have a prime number of marbles.

**Q.**

The simplest form of 10951168 is

(a) 1726 (b) 2526 (c) 1316 (d) 1516

**Q.**

Express 7429 as a product of its prime factors.

**Q.**

Why is 1 neither prime nor composite numbers?

**Q.**

Is $0$ an even number?

**Q.**

Question 27

The number of distinct prime factors of the largest 4-digit number is

(A) 2

(B) 3

(C) 5

(D) 11

**Q.**The prime factorisation of 272 is

- 22×17
- 24×17
- 24×13

**Q.**

Find the common factors of:

35 and 50

**Q.**

Will division of a rational number by another rational number always give a rational number?

**Q.**

The sum of prime factors of 4620 is:

28

32

30

34

**Q.**

Question 5 (c)

Which of the following numbers are co-prime:

30 and 415

**Q.**Match the following:

1.Total number of factors of 360 | i) 78 |

2. Sum of all factors of 360 | ii) 1092 |

3.Sum of all odd factors of 360 | iii) 24 |

4.Sum of all even factors of 360 | iv) 1170 |

5.Product of all factors of 360 | v) 36012 |

- 1-v, 2-i, 3-iv, 4-iii, 5-ii
- 1-iii, 2-iv, 3-i, 4-ii, 5-v
- 1-ii, 2-v, 3-i, 4-iii, 5-iv
- 1-i, 2-iv, 3-iii, 4-ii, 5-v

**Q.**

'a' and 'b' are two positive integers such that the least prime factor of 'a' is 3 and the least prime factor of 'b' is 5.Then find the least prime factor of (a+b).