Prime Factorisation

Q.

What is a prime factorization of $1225$?

Q. Find the prime factorization of 42 using the factor tree.

1. 2 $\times$ 3 $\times$ 3
2. 2 $\times$ 3 $\times$ 7
3. 2 $\times$ 3 $\times$ 6
4. 2 $\times$ 3 $\times$ 7

Q. Prime factorization of $20$ is

1. $2\times 2\times 5$
2. $4\times 4\times 5$
3. $4\times 5$
4. $2\times 5$

Q. Find the least number must be multiplied with 3456such that tht product becomes a perfect cube

Q.

Prime factorize the following number: $53295$

Q.

State the following number as prime or composite: 17

Q. The sum of distinct prime factors of 30 is_______.

Q. 2 × 2 × 2 × 2 × are the prime factors of 96.

1. 6
2. 2 × 3
3. 2 × 6
4. 3 × 4
5. 2 × 4

Q. The prime factorisation of $180$ is

1. $4\times 9\times 5$
2. $2\times 2\times 3\times 3\times 5$
3. $4\times 3\times 3\times 5$
4. $2\times 2\times 3\times 5\times 5$

Q. Consider the statements regarding prime factorization:

Statement I: The factors in prime factorization of a number are prime numbers.

Statement II: The numbers, having composite numbers as factors, cannot be expressed as prime factorization.

1. Both the statements are correct.
2. Only Statement I is correct.
3. Only Statement II is correct.
4. None of the above.

Q. $3$ is the only prime factor of $18.$

1. True
2. False

Q. Prove that one of every three consecutive positive integer is divisible by $3$.

Q. The prime factors of $40$ are:

1. $2$
2. $4$
3. $5$
4. $8$

Q. What are prime numbers? Find the prime factorization of 2048. [4 marks]

Q. The side of some cubes are given below. Find their volumes.

(1) 2 m
(2) 5 m
(3) 8 cm
(4) 4 cm
(5) 10 cm

Q. A number equals the given product of relatively prime numbers: $3\times 4\times 49$
The prime factorization of the number is

1. $2\times 3\times 7$
2. $2\times 2\times 3\times 49$
3. $2\times 2\times 3\times 7\times 7$
4. None of the above.

Q. Write the natural numbers from 102 to 113. What fraction of them are prime numbers?
[2 marks]

Q. Is the prime factorisation of $28$ is $4\times 7?$

1. False
2. True

Q. Prime factor of $11$ is $11$.

1. No
2. Yes

Q. There are $105$ flower seeds that need to be planted in flower vases. Find the minimum number of flower vases required such that prime numbers of flower seeds can be planted in each vase evenly.

Q. Two numbers $X$ and $Y$ are given by $X=2\times 3\times 5$ and $Y=2\times 5\times 11.$ Then prime factorization of $X\cdot Y$ is

1. $2\times 3\times 5\times 11$
2. $2\times 3^2\times 5^2\times 11$
3. $2\times 3\times 5^2\times {11}^2$
4. $2^2\times 3\times 5^2\times 11$

Q. Area of a plot is $693{\text{m}}^2.$ It is known that the length of the plot is a prime number. Find the possible value(s) of the length.

1. $3\text{m}$
2. $7\text{m}$
3. $9\text{m}$
4. $11\text{m}$

Q. Simplify the following:
$\left(i\right)\sqrt{45}-3\sqrt{20}+4\sqrt{5}\left(ii\right)\frac{\sqrt{24}}{8}+\frac{\sqrt{54}}{9}\left(iii\right)4\sqrt{12}\times 7\sqrt{6}$