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\\February 16, 2024 2:20 PM Surender Prajapati Proof 5 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 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.
3 675 3 450
3 225 3 150
3 75 2 50 Remember
5 25 5 25 The HCF of two or more
5 5 5 5 numbers cannot be bigger
1 1 than any one of the numbers.
Factors of 675 = 3 × 3 × 3 × 5 × 5
Factors of 450 = 3 × 3 × 2 × 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 mangoes?
6. Find the largest possible length of a stick which can be used to measure 448 cm,
560 cm and 920 cm exactly.
Mathematics-5 71
