Prime and Composite Numbers

Q.

Look at several examples of rational numbers in the form $\frac{p}{q}(q\ne 0)$ where $p$ and $q$ are integers with no common factors other than $1$ and having terminating decimal representations (expansions). Can you guess what property $q$ must satisfy?

Q. By what number should 1365 be divided to get 31 as quotient and 32 as remainder?

1. 32
2. 43
3. 42
4. 33

Q. How to find LCM of π, 2π, [π÷3]?

Q. Two numbers are in the ratio 3:4 and their LCM is 120. The sum of the numbers is ________.

Q.

Which of the following fraction is a terminating decimal?

1. 

2. 

3. 

4. 

Q. Explain why 7 × 11 × 13 + 13 is a composite number.

Q. Find the number of prime factors of 5005.

1. 2

2. 3

3. 4

4. 5

Q. If $\frac{12}{q}$ is a terminating decimal number, then which of the following is a possible value of q?

1. 21
2. 7
3. 9
4. 15

Q.

Determine whether the integers in each of these sets are pair wise relatively prime.
$$\begin{array}{ll}\text{a)}11,15,19& \text{b)}14,15,21\\ \text{c)}12,17,31,37& \text{d)}7,8,9,11\end{array}$$

Q.

Question 6
Explain why $7\times 11\times 13+13$ and $7\times 6\times 5\times 4\times 3\times 2\times 1+5$ are composite numbers.

Q.

The principal of a school wishes to distributes $84$ balls and $108$ bats equally among number of boys. Find the Greatest number receiving the gifts in this ways.

Q.

Question 6
Explain why $7\times 11\times 13+13$ and $7\times 6\times 5\times 4\times 3\times 2\times 1+5$ are composite numbers.

Q. Explain why 7 × 11 × 13 + 13 is a composite number.

Q. How will you show that $(17\times 11\times 2)+(17\times 11\times 5)$ is a composite number? Explain.

Q. Can composite number can be expressed as a product of powers of primes.Give reasons

Q.

Explain why 7 × 11 × 13 + 13 is a composite number. [2 MARKS]

Q. Question 7
Explain why $3\times 5\times 7+7$ is a composite number.

Q.

1. Find the H.C.F. of the following numbers using prime factorization method:

(ii) $42,63$

Q.

Question 7
Explain why $3\times 5\times 7+7$ is a composite number.

Q. A composite number has exactly two factors.

1. True
2. False

Q. is a prime factor of 125.

1. 25
2. 1
3. 5

Q. $(7\times 5\times 3\times 2+3)$ is a ________ number.

1. prime
2. composite
3. co-prime
4. even

Q. If $\frac{12}{q}$ is a terminating decimal number, then which of the following is a possible value of q?

1. 7
2. 9
3. 15
4. 21

Q.

Which of the following fraction is terminating decimal?

1. 

2. 

3. 

4. 

Q. If $2200=2^a\times 5^b\times {11}^c\times 3^d,$ then $a+b-c+d=$ .

1. 4
2. 2
3. 5
4. 3

Q. The sum of three non-zero prime numbers is 100. One of them exceeds the other by 36. Find the largest number.

1. 73
2. 91
3. 67
4. 57

Q. Prove that $(4-5\sqrt{2})$ is an irrational number.

Q. Explain why $7\times 11\times 13+13$ and $7\times 6\times 5\times 4\times 3\times 2\times 1+5$ are composite numbers.

Q. A composite number has exactly two factors.

1. True
2. False

Q.

Question 7
Explain why $3\times 5\times 7+7$ is a composite number.