Mathematics
Euclid’s Division Lemma
Practice questions
What are the Euclidean quotient and remainder when 314 is divided by 27?If a number leaves remainder 0 when divided by 23, what is its form?Which option gives the valid Euclidean form of dividing 98 by 15?If (a=9q+r), how many possible values can (r) have?If 1000 is divided by 64, what is the remainder?Which form is impossible when a positive integer is divided by 4?A number is of the form (6q+5). What will be the remainder of its square when divided by 6?If a number leaves remainder 6 when divided by 7, what is the remainder when 1 is added to it and then divided by 7?A number leaves remainder 5 when divided by 8. What is the remainder when 11 is added to the number and it is divided by 8?If (a=13q+9), what is the remainder when (a+20) is divided by 13?If (x) leaves remainder 7 when divided by 10, what is the remainder when (3x) is divided by 10?If a number leaves remainder 8 when divided by 11, what remainder will twice the number leave when divided by 11?Which option cannot be a valid value of (r) in (a=5q+r)?If (p) leaves remainder 4 when divided by 6, what is the remainder when (p^2) is divided by 6?Why can one of three consecutive integers be taken as of the form (3q)?If (m=4q+3), in which form can (m+1) be written?Which number gives quotient 24 and remainder 17 when divided by 18?If a number gives quotient 31 when divided by 21, what is the least possible value of that number?If a number gives quotient 31 when divided by 21, what is the greatest possible value of that number?If (a) and (b) are positive integers and (a=bq+r), which option satisfies the lemma?