# NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.3

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.3 (Ex. 3.3) Playing with Numbers in Hindi Medium and English Medium updated for new CBSE Session 2020-2021. Videos solution of all the questions of 6th Maths exercise 3.3

3 is also given question by question. PDF solutions are also available in Hindi and English Medium.## Class 6 Maths Chapter 3 Exercise 3.3 Solution

Class: 6 | Mathematics |

Chapter: 3 | Playing with Numbers |

Exercise: 3.3 | Solutions in Hindi and English Medium |

### CBSE NCERT Class 6 Maths Chapter 3 Exercise 3.3 Solution in English and Hindi Medium

### Class 6 Maths Chapter 3 Exercise 3.3 Solution in Videos

#### Prime Factorization

When we express a number as a product of its factors, we say that we have the number. For example, the number 24 can be factorized as:

(i) 24 = 2 × 12

(ii) 24 = 3 × 8

(iii) 24 = 4 × 6

(iv) 24 = 2 × 2 × 2 × 3

These factorizations are of different types. In the first and second factorizations, one factor is prime and the another factor is a composite number. In third factorization, both the factors are composite numbers. However, in fourth factorization, all the factors are prime numbers.

The process of expressing a given number as a product of prime factors is called prime factorization of the given number.

From the utility point of view, it is the prime factorization which is important than any other factorization. A number may not have a factorization with one or more composite factors, but it always has a prime factorization. Numbers 19 or 35 have no factorization in which a composite factor occurs. But they do have a prime factorization.

For example, 19 = 19 × 1 and 35 = 7 × 5.

## Factorize 468 into prime factors. We use the division method as shown on the right:

We can write, 468 = 2 × 2 × 3 × 3 × 13. Thus, the prime factorization of 468 is 2 × 2 × 3 × 3 × 13. The process can also be depicted in factor tree as follows: Image

##### Fundamental Theorem of Prime Factorization

There may be several factors of a number in which one or more factors are composite as we have observed in the case of number 24. However, there is only one factorization which has all factors prime. Here, we do not distinguish between the factorization 3 × 2 × 2 × 2, 2 × 2 × 3 × 2 and 2 × 2 × 2 × 3 as we know that 2 × 3 = 3 × 2. Thus, the order of the factors in which they appear in the factorization is ignored. We thus have a property called prime factorization property or the fundamental theorem of Arithmetic, which states that Every composite number has one and only one prime factorization.

The usual method of finding the prime factors of a number is to perform successive divisions, the first divisor being the least prime number from the factors of that number. Study the following examples.

##### what is prime factorization? Explain with the help of example.

Prime Factorization

When we express a number as a product of its factors, we say that we have the number. For example, the number 36 can be factorized as:

36 = 2 x 18 = 2 x 2 x 9 = 2 x 2 x 3 x 3

##### Write the smallest 4-digit number and express it as a product of primes. Ans.:

The smallest 4-digit number is 1000. The prime factorization of this is

1000 = 2 x 500 = 2 x 2 x 250 = 2 x 2 x 2 x 125 = 2 x 2 x 2 x 5 x 25 = 2 x 2 x 2 x 5 x 5 x 5

##### Find the smallest number having four different prime factors.

The smallest number having four different prime factor may be 2 x 3 x 5 x 7 = 210