Mathematics
Euclid’s Division Lemma
Practice questions
Which option gives the correct (q) and (r) for (511=23q+r)?If a number gives quotient 16 and remainder 44 when divided by 45, what is the number?If (a) leaves remainder 3 when divided by 16 and (b) leaves remainder 9 when divided by 16, what is the remainder when (a-b) is divided by 16?Why is at least one number among six consecutive integers divisible by 6?If a number leaves remainder 34 when divided by 35, what is the remainder when 71 is added to it and the result is divided by 35?If (u=12q+5), what is the remainder when (u^2-u) is divided by 12?A number leaves remainder 7 when divided by 9. What is the remainder when its fourth power is divided by 9?If a number leaves remainder 12 when divided by 18, what is the remainder after adding 6 to it?If (a=14q+9) and (b=14p+6), what is the remainder when (ab+a) is divided by 14?Which option gives the correct Euclidean form of dividing (1201) by (120)?If a number leaves remainder 1, 3, 5, or 7 when divided by 8, what is the remainder when its square is divided by 8?If a number leaves remainder 5 when divided by 27, what is the remainder when 8 times the number is divided by 27?If (a=7q+3), what is the remainder when (a^2+2) is divided by 7?If (a) leaves remainder 6 when divided by 11 and (b) leaves remainder 8 when divided by 11, what is the remainder when (3a+b) is divided by 11?A number leaves remainder 41 when divided by 42. What is the remainder when 85 is added to the number and the result is divided by 42?If an integer leaves remainder 3 when divided by 4, what is the remainder when (n^2+n+1) is divided by 4?If (a=30q+23), what is the remainder when (6a) is divided by 30?If (r) is the remainder and the divisor is 63, which of the following is not a valid value of (r)?If (n=10q+9), what is the remainder when (n^2+2n+1) is divided by 10?If (a=21q+17) and (b=21p+19), what is the remainder when (a+b+6) is divided by 21?