Prime Factorisation

Q.

${105}^2$ is equivalent to ___

Q. Which among the following is/are the prime factors of 125?

1. 25
2. 1
3. 125
4. 5

Q. Which of the following represents the correct prime factorisation of 272?

1. $2^2\times 3^2\times 13$

2. $2^4\times 17$

3. $3^3\times 13$

4. $2\times 3\times 7\times 11$

Q.

The number of ways in which 48 can be expressed as a product of it primes is (not considering the order in which these primes occur)

1. two

2. many

3. four

4. one

Q.

For any positive integer , $n^3-n$ is always divisible by ___?

1. 12

2. 15

3. 6

4. 18

Q.

The number of factors of $2^1{.3}^2{.5}^3$ are

1. 24

2. 48

3. 36

4. 12

Q.

If $132300=2^2\times 3^3\times 5^2\times a^b,$ then which of the following is true ?

1. $a=2b$

2. $a+b=8$

3. LCM of $a$ and $b$ is 14.

4. $a=b$

Q.

The sum of prime factors of 4620 is:

1. 30

2. 28

3. 32

4. 34

Q.

Express 5005 as a product of its prime factors.

Q.

Prime factorization of 1400:

1. ${2.3}^2{.5}^3$

2. $2^3.5.7$

3. $2^3{.5}^2{.7}^2$

4. $2^3{.5}^2.7$