Mathematics
Euclid’s Division Lemma
Practice questions
If a number leaves remainder 1 or 5 when divided by 6, what is the remainder when its square is divided by 6?If a number leaves remainder 4 when divided by 22, what is the remainder when 7 times the number is divided by 22?If (a=5q+2), what is the remainder when (a^2+1) is divided by 5?If (a) leaves remainder 4 when divided by 9 and (b) leaves remainder 7 when divided by 9, what is the remainder when (2a+b) is divided by 9?A number leaves remainder 29 when divided by 30. What is the remainder when 61 is added to the number and the result is divided by 30?If an integer leaves remainder 2 when divided by 3, what is the remainder when (n^2+n+1) is divided by 3?If (a=24q+17), what is the remainder when (5a) is divided by 24?If (r) is the remainder and the divisor is 41, which of the following is not a valid value of (r)?If (n=8q+7), what is the remainder when (n^2+2n+1) is divided by 8?If (a=18q+13) and (b=18p+16), what is the remainder when (a+b+7) is divided by 18?According to Euclid’s division lemma, what are the quotient and remainder when 1365 is divided by 112?If a number gives quotient 22 when divided by 39, what is the greatest possible value of that number?If a number gives quotient 18 when divided by 57, what is the least possible value of that number?Which option gives the correct Euclidean form of dividing 947 by 73?If (x=26q+25), what is the remainder when (x+28) is divided by 26?If (n) leaves remainder 8 when divided by 19, what is the remainder when (5n+7) is divided by 19?If a number leaves remainder 9 when divided by 11, what is the remainder when its square is divided by 11?Which is the correct list of all possible forms of a positive integer when divided by 9?If (a=31q+30), what is the remainder when (a+1) is divided by 31?If (m) leaves remainder 4 when divided by 17, what is the remainder when (m-23) is divided by 17?