Mathematics
Euclid’s Division Lemma
Practice questions
If a number leaves remainder 1, 3, 7, or 9 when divided by 10, what possible remainders can its square have when divided by 10?If a number leaves remainder 8 when divided by 39, what is the remainder when 11 times the number is divided by 39?If (a=12q+7), what is the remainder when (a^2+5) is divided by 12?If (a) leaves remainder 9 when divided by 17 and (b) leaves remainder 13 when divided by 17, what is the remainder when (4a+3b) is divided by 17?A number leaves remainder 57 when divided by 58. What is the remainder when 175 is added to the number and the result is divided by 58?If an integer leaves remainder 4 when divided by 5, what is the remainder when (n^2+n+1) is divided by 5?If (a=42q+31), what is the remainder when (8a) is divided by 42?If (r) is the remainder and the divisor is 97, which of the following is not a valid value of (r)?If (n=14q+13), what is the remainder when (n^2+2n+1) is divided by 14?If (a=33q+29) and (b=33p+31), what is the remainder when (a+b+6) is divided by 33?According to Euclid’s division lemma, what are the correct quotient and remainder when 3876 is divided by 173?If a number gives quotient 41 when divided by 73, what is the greatest possible value of that number?If a number gives quotient 19 when divided by 118, what is the least possible value of that number?Which option gives the correct Euclidean form of dividing 4555 by 289?If (x=52q+49), what is the remainder when (x+111) is divided by 52?If (n) leaves remainder 23 when divided by 31, what is the remainder when (8n+17) is divided by 31?If a number leaves remainder 14 when divided by 17, what is the remainder when its square is divided by 17?Which is the correct list of all possible forms of a positive integer when divided by 13?If (a=83q+82), what is the remainder when (a+1) is divided by 83?If (m) leaves remainder 9 when divided by 43, what is the remainder when (m-95) is divided by 43?