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\\December 6, 2023 12:53 PM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

Example 3: Find the prime factorisation of 80 by using division method.
Solution: To find the prime factorisation of 80, we follow the given steps:

Step 1: Divide 80 by the smallest prime number 2, mentally write 2 80
the quotient 40 below 80. 2 40
Step 2: Again, divide 40 by 2. Write the quotient 20 below 40. 2 20

Step 3: Continue the process, till we get the quotient as a prime 2 10
number. Here it is 5. 5
Step 4: Express 80 as a product of all divisors and the last quotient.

Thus, the prime factorisation of 80 = 2 × 2 × 2 × 2 × 5.

Practice time 5D

1. identify whether the following numbers is a prime or composite number.
(a) 15 (b) 21 (c) 23 (d) 33 (e) 46 (f) 49
2. Write all the prime numbers between:

(a) 10 and 30 (b) 50 and 60 (c) 80 and 90

3. how many composite numbers are there between two given numbers?
(a) 1 and 10 (b) 20 and 30 (c) 70 and 80
4. Complete the factor tree by filling the missing factors.

(a) 30 (b) 63 (c) 100

× 3 9 × ×

×
2 × ×

×
5. Fill in the boxes to complete the prime factorisation by division method.

(a) (b) (c)
75 2 625

25 2 54

9 5

3
6. Find the prime factorisation of the following numbers.

(a) 18 (b) 20 (c) 32
(d) 42 (e) 60 (f) 81

Mathematics-4 101