Question

Find the greatest number that will divide 445 572 and 699 leaving the remainder 4 ,5 ,
6 respectively

Answer 1

Answer

Solution

♦ Let the number be "x"

♦ Then According to the question

• 455 ÷ x = x(n) + 4

• 572 ÷ x = x(n) + 5

• 699 ÷ x = x(n) + 6

♦ So we can say that

(445 - 4 ) , ( 572 - 5) and ( 699 - 6 ) is divisible by x

♦ So Numbers divisible by "x"

>> 441

>> 567

>> 693

♦ Now we have to find HCF of above in order to find out "x"

♦ Prime factorization of above

441 = 7 × 7 × 3 × 3

567 = 7 × 3 × 3 × 3 × 3

693 = 11 × 7 × 3 × 3

♦ So HCF = 7 × 3 × 3

= 63

♦ So the greatest number = 63

Answer 2

your answer is in the attachment

hope it helps