# EUCLID DIVISION ALGORITHM QUESTIONS

## About "Euclid Division Algorithm Questions"

Word Problems Based on Division Algorithm :

Here we are going to see, word problems based on division algorithm.

(1) Find all positive integers, when divided by 3 leaves remainder 2.       Solution

(2)  A man has 532 flower pots. He wants to arrange them in rows such that each row contains 21 flower pots. Find the number of completed rows and how many flower pots are left over.     Solution

(3)  Prove that the product of two consecutive positive integers is divisible by 2.     Solution

(4)  When the positive integers a, b and c are divided by 13, the respective remainders are 9,7 and 10. Show that a+b+c is divisible by 13.     Solution

(5)  Prove that square of any integer leaves the remainder either 0 or 1 when divided by 4.          Solution

(6)  Use Euclid’s Division Algorithm to find the Highest Common Factor (HCF) of

(i) 340 and 412

(ii) 867 and 255

(iii)  10224 and 9648

(iv) 84, 90 and 120

(7)  Find the largest number which divides 1230 and 1926 leaving remainder 12 in each case.           Solution

(8)  If d is the Highest Common Factor of 32 and 60, find x and y satisfying d = 32x + 60y .          Solution

(9)  A positive integer when divided by 88 gives the remainder 61. What will be the remainder when the same number is divided by 11?          Solution

(10)  Prove that two consecutive positive integers are always coprime.          Solution After having gone through the stuff given above, we hope that the students would have understood, "Euclid Division Algorithm Questions".

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WORD PROBLEMS

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OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 