Find greatest no. That will divide 445,572&699 leaving remainder 4,5&6

1.	Find greatest no. That will divide 445,572&699 leaving remainder 4,5&6 respectively
Answer» We have to find the greatest number that divides 445, 572 and 699 and leaves remainders of 4, 5 and 6 respectively. This means when the number divides 445, 572 and 699 leaves remainders 4, 5 and 6 is that445 - 4 = 441, 572 - 5 = 567 and 699 - 6 = 693 are completely divisible by the required number.For the highest number which divides the above numbers can be calculated by HCF .Therefore, the required number is the H.C.F. of 441, 567 and 693 Respectively.First, consider 441 and 567.By applying Euclid’s division lemma, we get567 = 441 {tex}\\times{/tex}\xa01 + 126441 = 126 {tex}\\times{/tex}\xa03 + 63126 = 63 {tex}\\times{/tex}\xa02 + 0.Therefore, H.C.F. of 441 and 567 = 63Now, consider 63 and 693again we have to apply Euclid’s division lemma, we get693 = 63 {tex}\\times{/tex}\xa011 + 0.Therefore, H.C.F. of 441, 567 and 693 is 63Hence, the required number is 63. 63 is the highest number which divides 445,572 and 699 will leave\xa04,5 and 6 as remainder respectively.

Find greatest no. That will divide 445,572&699 leaving remainder 4,5&6 respectively