For an integer n , let S n = n + 1 , n + 2 , … . , n + 18 . Which of the following is true for all n ≥ 10 ?

S n has at least four multiples of 5

EASY

Earn 100

How do you express $375$ as a product of its prime factors in index form?

50% studentsanswered this correctly

Important Questions on Prime Time

EASY

Mathematics>Algebra>Prime Time>Prime Factorisation

Find the smallest positive integer

n \geq 10

such that

n + 6

is a prime and

9 n + 7

is a perfect square.

EASY

Mathematics>Algebra>Prime Time>Prime Factorisation

A two-digit number

\bar{a b}

is called almost prime if one obtains a two-digit prime number by changing at most one of its digits

a & b

. (For example, 18 is an almost prime number because 13 is a prime number). Then the number of almost prime two-digit numbers is

EASY

Mathematics>Algebra>Prime Time>Prime Factorisation

There are four prime numbers written in ascending order. The product of the first three is

385

and that of the last three is

1001 .

The last number is :

HARD

Mathematics>Algebra>Prime Time>Prime Factorisation

The prime numbers

a, b

and

c

are such that

a + b^{2} = 4 c^{2} .

Determine the sum of all possible values of

a + b + c .

MEDIUM

Mathematics>Algebra>Prime Time>Prime Factorisation

For an integer

n

, let

S_{n} = \{n + 1, n + 2, \dots ., n + 18\}

. Which of the following is true for all

n \geq 10

HARD

Mathematics>Algebra>Prime Time>Prime Factorisation

Let

N

denote the number of all natural numbers

n

such that

n

is divisible by a prime

p > \sqrt{n}

and

p < 20 .

What is the value of

N ?

EASY

Mathematics>Algebra>Prime Time>Prime Factorisation

A prime number

p

is called special if there exist primes

p_{1}, p_{2}, p_{3}, p_{4}

such that

p = p_{1} + p_{2} = p_{3} - p_{4} .

The number of special primes is

EASY

Mathematics>Algebra>Prime Time>Prime Factorisation

Express

120

as a product of its prime factors.

EASY

Mathematics>Algebra>Prime Time>Prime Factorisation

Which of the following number is an odd and prime number?

EASY

Mathematics>Algebra>Prime Time>Prime Factorisation

The sum of the squares of the digits of the largest two-digit prime number is:

EASY

Mathematics>Algebra>Prime Time>Prime Factorisation

a

and

b

are positive integers such that

a^{2} - b^{2}

is a prime number, then

a^{2} - b^{2}

is equal to:

HARD

Mathematics>Algebra>Prime Time>Prime Factorisation

The number of

6

-digit numbers of the form

a b a b a b

(in base

10

) each of which is a product of exactly

6

distinct primes is

EASY

Mathematics>Algebra>Prime Time>Prime Factorisation

It is given that the number

43361

can be written as a product of two distinct prime numbers

p_{1}, p_{2} .

Further, assume that there are

42900

numbers which are less than

43361

and are co-prime to it. Then,

p_{1} + p_{2}

MEDIUM

Mathematics>Algebra>Prime Time>Prime Factorisation

Consider the set

E = {5, 6, 7, 8, 9} .

For any partition

{A, B}

E,

with both

A

and

B

non-empty, consider the number obtained by adding the product of elements of

A

to the product of elements of

B .

Let

N

be the largest prime number among these numbers. Find the sum of the digits of

N .

EASY

Mathematics>Algebra>Prime Time>Prime Factorisation

Express

120

as a product of its prime factors.

EASY

Mathematics>Algebra>Prime Time>Prime Factorisation

The number of prime numbers which are less than

100

is:

HARD

Mathematics>Algebra>Prime Time>Prime Factorisation

For

a, b \in \{0, 1, \dots, 9\}

, a two digit number

a b

is defined for

10 a + b

. A two digit number

a b

is called a special prime if both

a b

and

b a

are primes. Then the total number of special primes is

EASY

Mathematics>Algebra>Prime Time>Prime Factorisation

Which of the following is not a pair of prime numbers ?

HARD

Mathematics>Algebra>Prime Time>Prime Factorisation

Suppose

a, b, c

are positive integers such that

2^{a} + 4^{b} + 8^{c} = 328 .

Then

\frac{a + 2 b + 3 c}{a b c}

is equal to-

EASY

Mathematics>Algebra>Prime Time>Prime Factorisation

a

and

b

are positive integers such that

(a^{2} - b^{2})

is a prime number, then

How do you express 375 as a product of its prime factors in index form?

Important Questions on Prime Time

Learn and Prepare for any exam you want !

How do you express $375$ as a product of its prime factors in index form?