Mathematics
Euclid’s Division Lemma
Practice questions
If (N) leaves remainder 30 when divided by 37, what is the remainder when (N+81) is divided by 37?Which option shows an invalid remainder for Euclid’s division lemma when the divisor is 46?If 5289 is divided by 211, what is the remainder?If (t=26q+19), what is the remainder when (4t+11) is divided by 26?If a number leaves remainder 9 when divided by 52, what is the remainder when nine times the number is divided by 52?Why is at least one number among seven consecutive integers divisible by 7?If a number is of the form (8q+3) or (8q+5), what is the remainder when its square is divided by 8?If (a=59q+44), what is the remainder when (a-103) is divided by 59?A number leaves remainder 17 when divided by 21. What is the remainder when its square is divided by 21?If (x=10q+9), what is the remainder when (x^2+x) is divided by 10?Which option gives the correct (q) and (r) for (2026=89q+r)?If a number gives quotient 24 and remainder 75 when divided by 76, what is the number?If (a) leaves remainder 5 when divided by 27 and (b) leaves remainder 14 when divided by 27, what is the remainder when (a-b) is divided by 27?Why is at least one number among eight consecutive integers divisible by 8?If a number leaves remainder 43 when divided by 44, what is the remainder when 133 is added to it and the result is divided by 44?If (u=15q+8), what is the remainder when (u^2-u) is divided by 15?A number leaves remainder 7 when divided by 13. What is the remainder when its fourth power is divided by 13?If a number leaves remainder 17 when divided by 24, what is the remainder after adding 31 to it?If (a=16q+11) and (b=16p+14), what is the remainder when (ab+a) is divided by 16?Which option gives the correct Euclidean form of dividing (5001) by (500)?