Question

Find the greatest number that will divide 455, 582 and 710 leaving remainders 14,

15 and 17 respectively​

Answer 1

Answer:

the greatest number that will divide 455, 582 and 710 leaving remainders 14, 15 and 17 respectively is 63.

455, 582 and 710 minus 14, 15 and 17 respectively is 441,567 and 693.

hcf of455, 582 and 710 is 63.

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Answer 2

Answer: The greatest number is 63

Step-by-step explanation:

Let the greatest number that will divide 455, 582 and 710 leaving remainders 14, 15 and 17 respectively​ be z.

Remainder when 455 is divided by z = 14

Number which is exactly divisible by z  =  455 - 14

Number which is exactly divisible by z  =  441

Remainder when 582 is divided by z = 15

Number which is exactly divisible by z  =  582 - 15

Number which is exactly divisible by z  =  567

Remainder when 710 is divided by z = 17

Number which is exactly divisible by z  =  710 - 17

Number which is exactly divisible by z  =  693

∴ z = HCF of 441, 567 and 693

441  =  3 × 3 × 7 × 7

567 =  3 × 3 × 3 × 3 × 7

693 =  3 × 3 × 7 × 11

HCF = 3 × 3 × 7

HCF = 63

∴ z = 63

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