Basics of Number Theory

The greatest number of $5$ digit which starts from $8$ and ends with $7$ is _____

The sum of five consecutive odd numbers is $265$. What is the sum of the largest number and twice the smallest number?

Find the largest given prime number. In four consecutive prime numbers that are in descending order, the product of the first three is $2431$ and that of the last three is $1001$.

How many mm represent $1 \mathrm{km}$?

Find the digit in the unit's place of the product $49237 \times 3995 \times 738 \times 83 \times 9$.

If a quantity is divided in the ratio $3:5$, the larger part is $75$. Find the quantity.

Find the smallest number from the given options which when divided by$25, 40$ or $56$ has$13$ as remainder in each case.

When $x^m$ is multiplied by $x^n$, the product is $1$. Find the relation between $m$ and $n$

A number $N$ is a positive three-digit number If $x$ is at its hundred's place and $y$ is at its unit's place, then the number $N-100x-y$is always divisible by

The least number which must be added to the greatest number of $4$ digits in order that the sum may be exactly divisible by $307$ is

$108.56$ can be written in words as:

The greatest number among $$\sqrt { 5 } ,\sqrt [ 3 ]{ 4 } ,\sqrt [ 5 ]{ 2 } ,\sqrt [ 7 ]{ 3 } $$ is

Which of the following number is multiple of $8$?

The absolute value of $-11$ is:

It is given that $(2^{32} +1)$ is exactly divisible by a certain number. Which of the following is also definitely divisible by the same number?

State the property used statement
$(29\times 36)\times 18=29\times (36\times 18)$

If the numerator of a fraction is increased by $800\%$ and the denominator is increased by $300\%$, then the resultant fraction is $1\frac{2}{7}$. What was the original fraction?

When $1787$ is rounded off to the nearest tens, we get:

Find the unit digit in $(81678{)}^{199}$:

Insert, commas suitably according to Indian system of numeration in $98432701$.