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

Answer: (a)

Required number = HCF of 200 and 320 = 40

Illustration :

Answer: (d)

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 411 – 3 = 408; 684 – 4 = 680 and 821 – 5 = 816

HCF of 408 and 816 = 408

HCF of 408 and 680

∴ Required number = 136

Answer: (c)

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).)

The number will be HCF of

307 – 3 = 304 and 330 – 7 = 323.

∴ Required number = 19

Answer: (d)

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 (989 – 5) and (1327 – 7)

= HCF of 984 and 1320 = 24

∴ HCF = 24

Answer: (b)

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

Illustration :

HCF of 15 and 300 = 15

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