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\\October 8, 2025 12:13 PM Bharat Arora P-9 Reader _________________________ Date: ___________________74

example 4: 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 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 the HCF of 675 and 450.
3 675 2 450
3 225 3 225
3 75 3 75 Math Insight
5 25 5 25 The HCF of two or more
5 5 5 5 numbers will always be equal
1 1 to or less than the smallest

Factors of 675 = 3 × 3 × 3 × 5 × 5 of them.
Factors of 450 = 2 × 3 × 3 × 5 × 5
The common factors of 675 and 450 are 3, 3, 5 and 5.

So, HCF of 675 and 450 = 3 × 3 × 5 × 5 = 225.
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

3. Find the HCF using the prime factorisation method.
( a) 15, 24 (b) 18, 90 (c) 32, 40 (d) 42, 56
( e) 15, 95 (f) 72, 80 (g) 12, 24, 48 (h) 22, 33, 66

( i) 24, 36, 56 (j) 22, 66, 99 (k) 25, 40, 65 (l) 48, 72, 96

4. Find the HCF using the long division method.
( a) 21, 63 (b) 35, 49 (c) 92, 132 (d) 36, 54, 72

( e) 132, 140, 250 (f) 165, 285, 205 (g) 164, 180, 112 (h) 285, 350, 1875

5. A fruit seller has 1320 apples and 1480 mangoes. He wants to put them in baskets.
What is the greatest number of baskets required, if each basket has the same number
of apples and the same number of mangoes?

6. Find the largest possible length of a stick which can be used to measure 448 cm,
560 cm and 920 cm exactly.

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