Prime Numbers

Q.

Which of the following numbers are co-prime:

1. $18\mathrm{and}35$

2. $15\mathrm{and}37$

3. $30\mathrm{and}415$

4. $17\mathrm{and}168$

5. $216\mathrm{and}215$

6. $81\mathrm{and}16$

Q. If the difference between two prime numbers is 2, then they are known as

1. twin primes
2. alternate primes
3. additive primes

Q.

What is the next number? $2,3,5,7,11,?,17$.

1. $12$

2. $13$

3. $14$

4. $15$

Q.

Express following prime number as the sum of three primes - :

$29=...........+............+............$

Q. Explain why 5*7*11*13*17+17 is a composite number

Q. The number of distinct primes in the prime factorization of 32760 A. 8 B. 6 C. 13 D. None of these

Q. Which of the following is a prime number?

1. 42
2. 46
3. 23
4. 26

Q.

Express following prime number as the sum of three primes - :

$37=.........+..........+........$

Q.

Find the common factors of $56$ and $120$.

Q. Explain why 5*7*11*13*17+17 is a composite number

Q.

Identify the Theorem:Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.

1. Theorem of factorization

2. Composite Theorem

3. Euclid’s Theorem

4. Fundamental Theorem of Arithmetic

Q. 54.The sum of three prime numbers is 100. If one of them exceeds another by 36, then find the numbers

Q. Every composite number can be factorised as a product of its primes, and this is unique, apart from the order in which the factors occur.

1. True
2. False

Q. It is Samaira's birthday, she has bought chocolates for all her 40 classmates, and each student has been given a position to sit which is labeled from 1 to 40. She has bought two kinds of chocolates, one Dairy Milk and the other Munch. She gives Dairy Milk to those who are at the seats labelled a prime number. How many children will get Dairy Milk chocolates?

1. 11

2. 12

3. 13

4. 21

Q.

The sum of prime factors of 4620 is:

1. 28

2. 34

3. 30

4. 32

Q. According to Euclid's Division Lemma, .

1. Remainder = Divisor
2. Remainder < Divisor
3. Remainder > Divisor

Q. According to Euclid's Division Lemma, .

1. Remainder = Divisor
2. Remainder < Divisor
3. Remainder > Divisor

Q. Every composite number can be factorised as a product of its primes, and this is unique, apart from the order in which the factors occur.

1. False
2. True

Q. check whether 12^n end with the digit 0 or 5 for any natural number N

Q. prove that a positive integer n is prime number if no prime p less than or equal to root n divides n

Q.

For what least value of n, where n is a natural number :

A.5^n is divisble by 3?

B.24^n is divisible by 8?

C.15^n is divisible by 5?

D.19^n is divisible by 9?

E.18^n is divisible by 6?

Q.

The sum of prime factors of 4620 is:

1. 30

2. 28

3. 32

4. 34

Q.

An example of twin primes is

1. $11,13$

2. $13,15$

3. $28,29$

4. $31,33$

Q.

The sum of prime factors of 4620 is:

1. 30

2. 28

3. 32

4. 34

Q.

Identify the Theorem:Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.

1. Composite Theorem

2. Euclid’s Theorem

3. Fundamental Theorem of Arithmetic

4. Theorem of factorization

Q.

All prime numbers are

1. odd

2. even

3. composite

4. odd except $2$

Q. Show that 571 is a prime number.

Q.

The sum of prime factors of 4620 is:

1. 30

2. 28

3. 32

4. 34