Page 49 - Start Up Mathematics_6

MATHS LAB ACTIVITY

Objective: Finding factors of a number using activity method

Material required: Cardboard, a pair of scissors, a pencil
Let’s find factors of a number, say 10.
Step 1: Cut 10 equal squares of appropriate size from a cardboard.

Step 2: Arrange the 10 squares in all possible ways to form a rectangle or a square.
(i)

(ii) (iii) (iv)

Observation: We observe that Fig. (i) has 1 row, Fig. (ii) has 2 rows, Fig. (iii) has 5 rows and
Fig. (iv) has 10 rows.
Inference: Number of rows in each arrangement are the factors of 10. Therefore, factors
of 10 are 1, 2, 5 and 10.
Verification: 1 is a factor of 10  10 ÷ 1 = 10
2 is a factor of 10  10 ÷ 2 = 5

5 is a factor of 10  10 ÷ 5 = 2
10 is a factor of 10  10 ÷ 10 = 1

Example 1: Write all the factors of the following numbers:

(a) 8 (b) 23 (c) 36 (d) 108
Solution: We write all possible ways in which each of the above numbers can be written as
the product of two numbers.
(a) Since, 8 = 8 × 1 8 = 4 × 2
Therefore, factors of 8 are 1, 2, 4 and 8.

(b) Since, 23 = 23 × 1
Therefore, factors of 23 are 1 and 23.
(c) Since, 36 = 36 × 1 36 = 18 × 2 36 = 12 × 3
36 = 9 × 4 36 = 6 × 6
Therefore, factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.

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