Mathematics
Euclid’s Division Lemma
Practice questions
Which option gives the correct (q) and (r) for (4097=137q+r)?If a number gives quotient 31 and remainder 95 when divided by 96, what is the number?If (a) leaves remainder 8 when divided by 35 and (b) leaves remainder 19 when divided by 35, what is the remainder when (a-b) is divided by 35?Why is at least one number among ten consecutive integers divisible by 10?If a number leaves remainder 61 when divided by 62, what is the remainder when 187 is added to it and the result is divided by 62?If (u=18q+11), what is the remainder when (u^2-u) is divided by 18?A number leaves remainder 10 when divided by 17. What is the remainder when its fourth power is divided by 17?If a number leaves remainder 29 when divided by 36, what is the remainder after adding 43 to it?If (a=20q+13) and (b=20p+18), what is the remainder when (ab+a) is divided by 20?Which option gives the correct Euclidean form of dividing (7001) by (700)?If a number leaves remainder 1, 5, 7, or 11 when divided by 12, what is the remainder when its square is divided by 12?If a number leaves remainder 11 when divided by 45, what is the remainder when 13 times the number is divided by 45?If (a=16q+9), what is the remainder when (a^2+7) is divided by 16?If (a) leaves remainder 11 when divided by 19 and (b) leaves remainder 16 when divided by 19, what is the remainder when (5a+4b) is divided by 19?A number leaves remainder 73 when divided by 74. What is the remainder when 223 is added to the number and the result is divided by 74?If an integer leaves remainder 5 when divided by 6, what is the remainder when (n^2+n+1) is divided by 6?If (a=48q+37), what is the remainder when (10a) is divided by 48?If (r) is the remainder and the divisor is 109, which of the following is not a valid value of (r)?If (n=22q+21), what is the remainder when (n^2+2n+1) is divided by 22?If (a=39q+35) and (b=39p+37), what is the remainder when (a+b+6) is divided by 39?