## Chapter 1 Simplification Prime And Composite Numbers Problems

**Question 1. What is the smallest prime number?**

**Solution:**

The smallest prime number is 2.

**Question 2. Which number is neither prime nor composite?**

**Solution:**

The number is 1, which is neither prime nor composite.

**Question 3. Examine whether the following pair of numbers are prime to each other**

**1. 5, 7 **

**Solution:**

**Class 6 Math Solution WBBSE In English**

**Given Numbers: 5, 7 **

5 and 7 have no common factor except 1,

∴ 5 and 7 are prime to each other.

**2. 10, 21.**

**Solution:**

10 = 2 x 5 and 21 = 3 x 7.

∴ The factors of 10 are 1, 2, 5, and 10.

Among them, 2 and 5 are the prime factors of

Again, the factors of 21 are 1, 3, 7, and 21.

Among them, 3 and 7 are the prime factors of 21.

∴ 10 and 21 have no common factor other than 1.

So 10 and 21 are prime to each other.

**Read And Learn More: WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Solved Problems**

**Example 4. Write two composite numbers which are prime to each other. **

**Class 6 Math Solution WBBSE In English**

**Solution:**

**Two composite numbers which are prime to each other**

** **Two composite numbers 18 and 35 are prime to other.

Because, 18 = 2 x 3 x 3 and 35 = 5 x 7.

So 18 and 35 have no common factor except 1.

∴ 18 and 35 are two composite numbers but are prime to each other.

**Example 5. Write down all the prime numbers between 100 and 200.**

**Solution:**

**The prime numbers between 100 and 200**

The prime numbers between 100 and 200 are as follows

101, 103, 107, 109, 113, 131, 133, 137, 139, 141, 149, 151, 157, 161, 163, 167, 173, 179, 181, 191, 193, 197, 199.

**Class 6 Math Solution WBBSE In English**

**Example 6. Find whether 331 is a prime number or not.**

**Solution:**

**Given:**

** 331**

Since 331 contains 1 in the unit’s place, therefore, 331 is not divisible

by any even number and also 331 is not divisible by 5.

Now the sum of the digits is 3+3 + 1 = 7. Therefore, the number 331 is not divisible by 3 or 9.

Now we divide the number 331 by 7, 11, 13, 17, etc., and we get,

The number 331 when divided by 19, the quotient is 17, which is less than the divisor 19, therefore further division by a prime number greater than 19 is not required.

**Simplification For Class 6**

∴ The number 331 is a prime number.

**Example 7. Find the prime factors of 30030.**

**Solution :**

**The prime factors of 30030**

**Simplification For Class 6**

∴ 30030 = 2 x 3 x 5 x 7 x 11 x 13

∴ The prime factors of 30030 are 2, 3, 5, 7, 11, and 13.

**Example 8. Find the common factor or factors of the numbers 154, 195, and 714 ****by resolving them into prime factors.**

**Solution:**

**Given:**

**The common factor or factors of the numbers 154, 195, and 714 ****by resolving them into prime factor**

∴ 154 = 1 X 2 x 7 x 11.

∴ 195 = 1 × 3 × 5 × 13

∴ 714 = 1 x 2 x 3 x 7 x 17.

Here we see that 154, 195, and 714 have no common factor except 1.

Therefore, 154, 195, and 714 are mutually prime to each other.

**Class 6 Math Solutions WBBSE English Medium**

**Example 9. Find the common factors of the numbers 42, 66, and 78. Obtain the highest common factors of them.**

**Solution:**

**The common factors of the numbers 42, 66, and 78.**

∴ 42 = 1 x 2 x 3 x 7.

∴ Factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.

∴ 66 1 × 2 × 3 × 11

∴ Factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66.

∴ 78 1 X 2 X 3 X 13

∴ Factors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78.

∴ The common factors of 42, 66, and 78 are: 1, 2, 3, 6

∴ Highest common factor

∴ The required highest common factor of the given numbers = 6.

**Class 6 Math Solutions WBBSE English Medium**

**Example 10. Examine, without actual division, whether the number 40821 is divisible by 3 or not.**

**Solution: **

We know that any number will be divisible by 3 if the sum of the digits of the number is divisible by 3.

Here is the sum of the digits of the numbers 408214+0+8+2+1 = 15, which is divisible by 3.

Hence the number 40821 is divisible by 33

**Example 11. Examine, without actual division, whether the number 55473 is divisible by 11 or not.**

**Solution: **

We know that any number will be divisible by 11 if the difference between the sum of the digits in the odd places and even places of the number be zero or divisible by 11.

Here, the sum of the digits in the even places of the number 55473 = 5 + 7 = 12, and the sum of the digits in the odd places of the number 55473 = 5 + 4 + 3 = 12.

The difference of the sum of the digits in the odd places and even places = 12 12 = 0.

Hence the number 55473 is divisible by 11.

**Example 12. Examine, without actual division, whether the number 908476118 is divisible by 11 or not.**

Solution:

We know that any number will be divisible by 11 if the difference between the sum of the digits in the odd places and even places of the number be zero or divisible by 11.

Here, the sum of the digits in the odd places of the number 908476118 9+ 8 + 7+1+8=33 and that of the digits in the even places of the number 908476118 = 1 + 6 + 4 + 0 = 11.

.. The difference of the sum of the digits in the odd places and even places = 33 11 22, which is divisible by 11.

Hence the number 908476118 is divisible by 11.

**Class 6 Math Solution WBBSE**

**Example 13. Without actual division, Examine**

**1. if the number 85944 is divisible by 4.**

**2. if the number 705432700 is divisible by 4.**

**Solution:**

We know that a given number is divisible by 4 if the last two digits, of the number, be zeroes or if the number formed by the last two digits of the given number is divisible by 4.

**1. if the number 85944 is divisible by 4.**

The number formed by the last two digits of the number 85944 is 44, which is divisible by 4.

∴ The number 85944 is divisible by 4.

**2. if the number 705432700 is divisible by 4.**

The last two digits of the number 705432700 are zeroes.

∴ The number 705432700 is divisible by 4.