Page 64 - ICSE Math 6

Example 26: Find the greatest number that will divide 90, 210 and 420 without leaving any remainder.

Solution: The required number is the HCF of 90, 210 and 420.
Since, 90 = 2 × 3 × 3 × 5
210 = 2 × 3 × 5 × 7
420 = 2 × 2 × 3 × 5 × 7

Common prime factors are 2, 3 and 5.
∴ HCF = 2 × 3 × 5 = 30

Example 27: Find the greatest number that will divide 139, 184 and 454 leaving the remainder 4 in
each case.

Solution: As 139 – 4 = 135, 184 – 4 = 180 and 454 – 4 = 450, therefore the required number is
the HCF of 135, 180 and 450.
Since, 135 = 3 × 3 × 3 × 5
180 = 2 × 2 × 3 × 3 × 5
450 = 2 × 3 × 3 × 5 × 5
Common prime factors are 3 and 5.

∴ HCF = 3 × 5 = 15

EXERCISE 4.5

1. Find the HCF of the following numbers using the common factor method.
(a) 25 and 30 (b) 40 and 58 (c) 60 and 112 (d) 216 and 174

(e) 165 and 81 (f) 275, 83 and 309 (g) 27 and 36 (h) 33 and 99
2. Find the HCF of the following numbers using the prime factorization method.

(a) 81 and 72 (b) 64 and 320 (c) 176 and 528 (d) 47 and 147
(e) 345 and 625 (f) 270, 480 and 1,350 (g) 120 and 24 (h) 135 and 675

3. Find the HCF of the following numbers using the division method.
(a) 459 and 270 (b) 504 and 663 (c) 221 and 1,105 (d) 1,362, 9,020 and 450

(e) 450, 360 and 9,000 (f) 275 and 309 (g) 270 and 1,350 (h) 3,315 and 663
4. Find the greatest number that will divide 345, 720 and 180 completely.

5. Find the greatest number that will divide 135, 401 and 268 leaving the remainder 2 in each case.
6. Dolly purchases two bags of fertilizer weighing 75 kg and 105 kg. Find the maximum value of
weight which can measure the two bags exact number of times.

Lowest Common Multiple (LCM)

The LCM of two or more numbers is the smallest common multiple of the given numbers. For example,
Multiples of 10 are 10, 20, 30, 40, 50, …

Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, …

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