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

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

EASY

Mathematics>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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 .

HARD

Mathematics>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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-

HARD

Mathematics>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

Express

120

as a product of its prime factors.

EASY

Mathematics>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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

EASY

Mathematics>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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

EASY

Mathematics>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

If

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>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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}

is

MEDIUM

Mathematics>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

Consider the set

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

For any partition

{A, B}

of

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>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

Express

120

as a product of its prime factors.

EASY

Mathematics>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

The number of prime numbers which are less than

100

is:

HARD

Mathematics>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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

MEDIUM

Mathematics>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

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

?

EASY

Mathematics>Arithmetic>The Number System>Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.

If

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 The Number System

Learn and Prepare for any exam you want !

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

Important Questions on The Number System

Learn and Prepare for any exam you want !

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