model 3 find hcf of numbers Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

First of all we find the HCF of 945 and 2475. HCF = 45

Illustration :

∴ Maximum number of animals in each flock = 45

Required total number of flocks = $945/45 + 2475/45$

= 21 + 55 = 76

Answer: (c)

Using Rule 7,

Let x be the remainder.

Then, (25 – x ), (73 – x ), and (97 – x )

Will be exactly divisible by the required number.

∴ Required number

= HCF of (73 –x ) – (25 –x ), (97 –x ) – (73 –x ) and (97 –x ) – (25 –x )

= HCF of (73 –25), (97 –73), and (97 –25)

= HCF of 48, 24 and 72 = 24

Answer: (b)

Required number = HCF of 390, 495 and 300 = 15

Illustration :

HCF of 15 and 300 = 15

Answer: (d)

Using Rule 7,

3026 –11 = 3015 and 5053 –13 = 5040

Required number = HCF of 3015 and 5040

∴ Required number = 45

Answer: (a)

Using Rule 7,

(The largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r). )

Required number

= HCF of 2300 – 32

= 2268 and 3500 – 56 = 3444

∴ HCF = 84

Answer: (a)

Length of the floor

= 15 m 17 cm = 1517 cm

Breadth of the floor

= 9m 2 cm = 902 cm.

Area of the floor

= 1517 × 902 $cm^2$

The number of square tiles will be least, when the size of each tile is maximum.

∴ Size of each tile = HCF of 1517 and 902 = 41

∴ Required number of tiles

=${1517× 902}/{41× 41}$ = 814