11+ Maths Solved Topic Wise Questions

1. Factors

Factors are the numbers that can divide another number without any remainder. Factors are a part of our daily life, such as dividing something into equal parts, comparing and exchanging money, making calculations and understanding time. For example, 6 can be factored as 1 × 6 and 2 × 3. Hence, the factors of 6 are 1, 2, 3 and 6.

1.1 Properties of Factors

The properties of factors are given below:

• 1 is a factor of every number.
• Every natural number is a factor of itself.
• Apart from 0 and 1, all the whole numbers have at least two factors.
• Zero is not a factor of any non-zero number.
• Other than zero, all integers are factors of zero. 
• Every factor is less than or equal to the given number.
• The number of factors of a given number is finite.

1.2 How to find Factors of a number?

Factors are the numbers you multiply together to get another number. We can use both "Division" and "Multiplication" to find the factors.

Factors by Division

To find the factors of a number using division, we follow these steps:

• Find all the numbers less than or equal to the given number.
• Divide the given number by each of the numbers.
• Factors are numbers that will divide into a whole number with no remainder.

For example, finding the factors of 8 using division.

The numbers less than or equal to 8 are 1, 2, 3, 4, 5, 6, 7 and 8. Dividing 8 by each of these numbers:

We can observe that divisors 1, 2, 4, and 8 give zero as the remainder. Thus, factors of 8 are 1, 2, 4, and 8.

Factors by Multiplication

To find the factors using the multiplication, we follow these steps:

• Write the number as the multiplication of two numbers in different possible ways.
• All these numbers in the multiplications are the factors of the given number.

For example, finding the factors of 24 using multiplication.

All the numbers that are involved in these multiplications are the factors of the given number. Thus, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.