Question

find the largest number which divides 445 and 572 and 699 leaving remainders 4 5 6 respectively​

Answer 1

Answer:

63 is the largest number.

Step-by-step explanation:

Its given that the required number when divides 445, 572 and 699 leaves remainders 4, 5 and 6  

This means 445 – 4 = 441, 572 – 5 = 561 and 699 – 6 = 693 are completely divisible by that number  

∴ The required number = HCF of 441, 567 and 693

Now find the HCF of those 3 numbers:  

441 = 3 x 3 x 7 x 7  

567 = 3 x 3 x 3 x 3 x 7  

693 = 3 x 3 x 7 x 11  

The common factors are 3 x 3 x 7 = 63  

HCF Of (441,567,693) = 63  

445 / 63 = 7 remainder 4  

572 / 63 = 9 remainder 5  

699 / 63 = 11 remainder 6

Therefore 63 is the largest number that will give the desired remainders