Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

MEDIUM

Earn 100

Express $5005$ as a product of its prime factors.

Important Questions on Real Numbers

MEDIUM

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

Check whether $6^{n}$ can end with the digit $0$ for any natural number $n$ .

EASY

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

Write the sum of the powers of the prime factors of

196

MEDIUM

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

Show that any positive even integer is of the form

4 q

or

4 q + 2

, where

q

is some integer.

MEDIUM

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

How many numbers lie between

100

and

400

which when divided by

9

leave a remainder

6

, and when divided by

21

, leave a remainder

12

?

EASY

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

Show that every positive odd integer is of the form $(4 q + 1)$ or $(4 q + 3)$ , where $q$ is some integer.

MEDIUM

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

If

\frac{3}{6 + 3 \sqrt{3}} = a + \sqrt{3} b

, where

a

and

b

are integers, then the value of

\sqrt{5 a + b}

is:

EASY

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

Show that any positive odd integer is of the form

4 q + 1

or

4 q + 3

where

q

is an integer.

HARD

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

If

a

and

b

are odd integers, then which of the following is an even integer?

EASY

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

The prime factors of

408

are

MEDIUM

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

Solve the quadratic equation $x^{2} - 9 = 0 .$

EASY

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

Product of any three consecutive even numbers is divisible by

EASY

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

The HCF of two co-prime numbers is :

EASY

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

By adding

1

to the sum of all natural numbers between

1

and

300

, which are divisible by

7

and

8

a number

p

is obtained then

+ \sqrt{p} =

_____

EASY

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

What is the exponent of

2

in the prime factorisation of

864 ?

EASY

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

Cube root of

328509

is

MEDIUM

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

The digit at the unit place in

{(3157)}^{2020}

is

EASY

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

Mr. Anil lives in village and is engaged in agriculture occupation. He needs some money and takes loan of Rs.

1, 00, 000

from co-operative bank situated in his village. He also borrows Rs.

50, 000

from money lender of the village and Rs.

25, 000

from his friend. In this situation, what is the ratio of his loan from formal and informal sector?

EASY

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

Express

5005

as a product of its prime factors.

EASY

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

The sum of all possible three-digit numbers formed by digits

3

,

0

and

7

, using each digit only once is:

MEDIUM

Mathematics>Arithmetic>Real Numbers>The Fundamental Theorem of Arithmetic

If $A$ is integer, $B$ is natural number then $B - A = ?$