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\\November 3, 2023 11:27 AM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

Solution:
(a) HCF of 594 and 252. (b) First find the HCF of 144 and 312.

252 594 2 144 312 2
– 504 – 288
90 252 2 24 144 6
– 180 – 144

72 90 1 0
– 72 HCF of 144 and 312 = 24
18 72 4 Now, we find HCF of 24 and 396.
– 72 24 396 16
0
– 384
12 24 2
– 24
0

Thus, HCF of 252 and 594 is 18. HCF of 24 and 396 is 12.

Thus, HCF of 144, 312 and 396 is 12.
Example 5: Two tankers contain 675 litres and 450 litres of water respectively. Find the

maximum capacity of a container which can measure the water of both the tankers exactly.
Solution: The maximum capacity of a container which can measure the water of both
the tankers when used an exact number of times will be the HCF of 675 and

450. So, we have to find HCF of 675 and 450.
Factors of 675 = 3 × 3 × 3 × 5 × 5 3 675 3 450
3 225
3 150
Factors of 450 = 3 × 3 × 2 × 5 × 5 3 75 2 50
The common factors of 675 and 450 are 3, 3, 5 and 5. 5 25 5 25

So, HCF of 675 and 450 = 3 × 3 × 5 × 5 = 225. 5 5 5 5
1
1
Thus, the maximum capacity of a container which can
measure the water of both the tankers is 225 litres.

Practice Time 3E

1. Find the common factors of the following numbers.

(a) 18, 24 (b) 21, 36 (c) 48, 56 (d) 72, 102
2. Find the HCF using the common factors method.

(a) 15, 20 (b) 12, 18 (c) 33, 55 (d) 35, 42

(e) 42, 64 (f) 50, 80 (g) 18, 24, 32 (h) 32, 48, 72
(i) 15, 30, 75 (j) 28, 42, 70 (k) 50, 75, 100 (l) 21, 56, 35

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