Mathematics
Euclid’s Division Lemma
Practice questions
If (N) leaves remainder 39 when divided by 47, what is the remainder when (N+102) is divided by 47?Which option shows an invalid remainder for Euclid’s division lemma when the divisor is 69?If 9876 is divided by 412, what is the remainder?If (t=46q+37), what is the remainder when (6t+17) is divided by 46?If a number leaves remainder 15 when divided by 73, what is the remainder when thirteen times the number is divided by 73?Why is at least one number among eleven consecutive integers divisible by 11?If a number is of the form (12q+5) or (12q+7), what is the remainder when its square is divided by 12?If (a=79q+61), what is the remainder when (a-140) is divided by 79?A number leaves remainder 27 when divided by 34. What is the remainder when its square is divided by 34?If (x=14q+13), what is the remainder when (x^2+x) is divided by 14?Which option gives the correct (q) and (r) for (6789=157q+r)?If a number gives quotient 27 and remainder 111 when divided by 112, what is the number?If (a) leaves remainder 10 when divided by 41 and (b) leaves remainder 23 when divided by 41, what is the remainder when (a-b) is divided by 41?Why is at least one number among twelve consecutive integers divisible by 12?If a number leaves remainder 85 when divided by 86, what is the remainder when 259 is added to it and the result is divided by 86?If (u=20q+13), what is the remainder when (u^2-u) is divided by 20?A number leaves remainder 12 when divided by 19. What is the remainder when its fourth power is divided by 19?If a number leaves remainder 37 when divided by 48, what is the remainder after adding 59 to it?If (a=24q+17) and (b=24p+22), what is the remainder when (ab+a) is divided by 24?Which option gives the correct Euclidean form of dividing (9001) by (900)?