Fundamental Theorem of Arithmetic

Q. State True or False
Every composite number can be factorised as a product of primes.

1. True
2. False

Q.

Every even positive integer is of the form (a) ___ and every positive odd integer is of the form (b) ___.
(x is any positive integer)

1. $a=2x^3,b=2x+2$
2. $a=2x^2,b=2x+1$
3. $a=2x,b=2x+1$
4. $a=x,b=3x+1$

Q.

If $p=2^a\times 3^b\times 5^c$ and $a>b>c$ are natural numbers, then what is the unit digit of p?

1. 0

2. 1

3. 2

4. 3

Q.

If 2 and 5 are factors of a number, what will be the unit’s digit of that number?

1. 0

2. 1

3. 2

4. 3

Q.

Check whether $6^n$ can end with the digit 0 for any natural number n. [2 MARKS]

Q.

For what value of ‘n’ would $4^n$ end with zero?

1. It will not end with zero for any value of n.

2. 10

3. 0

4. Can’t say

Q.

p = $2^2$.$3^2$.$q^2$ (where q is a prime $<$ 7) is the prime factorisation representation of ‘p’. What is the value of p?

1. p = 700

2. Can’t say

3. p = 36

4. p = 900

Q.

Consider the number $4^n$, where n is a natural number. Check whether there is any value of n for which $4^n$ ends with the digit zero. [2 MARKS]

Q.

Express as product of its prime factors : 156

Q.

${1400}^n$ is NOT divisible by which of the following, if n is a natural number:

1. 100

2. 175

3. 56

4. 210