Euclid's Division Algorithm

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

Find the largest number which divides $1230$ and $1926$ leaving remainder $12$ in each case.

Use Euclid's division algorithm to find the highest common factor $\left(\mathrm{HCF}\right)$ of $84, 90$ and $120$.

Use Euclid's division algorithm to find the highest common factor $\left(\mathrm{HCF}\right)$ of $10224$ and $9648$.

Use Euclid's division algorithm to find the highest common factor $\left(\mathrm{HCF}\right)$ of $867$ and $255$.

Use Euclid's division algorithm to find the highest common factor $\left(\mathrm{HCF}\right)$ of $340$ and $412$.

The HCF of two equal positive integers $k, k$ is _____.

Euclid's division algorithm is a repeated application of division lemma until we get remainder as _____. (Write the answer in words)

A milkman has $175 \mathrm{L}$ of cow's milk and $105 \mathrm{L}$ of buffalo's milk. He wishes to sell the milk by filling the two types of milk in cans of equal capacity. Calculate the capacity of the can. Express your answer in $\mathrm{L}$.

If $d$ is the Highest Common Factor of $32$ and $60$, find $x$ and $y$ satisfying $d=32x+60y$.

Prove that square of any integer leaves the remainder either $0$ or $1$ when divided by $4$.

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 $13$.

Prove that the product of two consecutive positive integers is divisible by $2$.

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.

If the H.C.F of $65$ and $117$ is expressible in the form of $65\mathrm{m}-117$, then the value of $m$ is