Factors of Natural Numbers

Q.

The numbers with more than two factors are called ________.

1. prime

2. composite

3. natural
4. integer

Q. The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then find the greater number.
___

Q. 72 as a product of its prime factors can be represented as ______ .

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

Q.

If x is a positive integer such that 2x+12 is perfectly divisible by x, then the number of possible values of x is

Q. Write down steps involved in splitting the middle term.

Q. Number of factors of 12 are

1. 1
2. 5
3. 12
4. 6

Q.

Factor completely $y^2+6y+8$.

Q.

An irreducible factor is a factor which cannot be expressed further as a____of factors.

1. Product or multiplication
2. Multiplication
3. Sum
4. Remainder

Q.

I am the smallest number, having four different prime factors. Can you find me?

Q.

What are the factors of $2450$?

Q.

Which of the following is a factor of 5xy?

1. $5x^2$

2. 4

3. xy

4. 2y

Q.

Write the factorisation of

$-3xyz$

Q. In factorisation how to find by L.C.M

Q. 72 as a product of its prime factors can be represented as ______ .

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

Q.

Factorise the expression:
$a{x}^2+b{y}^2+bxy+axy$

1. $(x+y)(ax+by)$

2. $(x-y)(ax-by)$

3. $(x+y)(ax-by)$

4. $(ax+by)(ax+by)$

Q.

State whether the given statement is true or false.
$\frac{(3x^2+1)}{\left(3x^2\right)}=1+1=2$.

1. True

2. False

Q. The smallest number having four different prime factors is

1. 105
2. 210
3. 16
4. 30

Q.

List all composite numbers from

$10$ to $18$

Q.

If AB is divisible by 5 but not by 2 and BA is divisible 3. Then which of the following is possible value of A and B?

a.A=5, B=2

b.A=4, B=5

c.A=7, B=5

d.A=4, B=0

Q.

Natural numbers having factors in addition to one and itself are called ______ numbers.

1. composite

2. prime

3. odd

4. even

Q. What is the least natural number you have to add 1024 to get multiple of 181 ?

Q.

Square root of 256 is __.

Q. Factorise the trinomial $2x^2+7x+6$.

Q. What is Composite number?

Q.

If is divisible by 11, find all possible values of a + b.

Q.

Identify terms and factors in the expressions given below:

$-4x+5$

Q. Factorize each of the following algebraic expressions: \(7a(2x-3) + 3b (2x - 3)\)

Q. How can we factorise trinomials?

Q.

33 is ______ number.

1. odd and prime

2. even and prime

3. odd and composite

4. even and composite

Q.

Write the smallest $5$-digit number and express as a product of prime numbers.