Question

A number which is a factor of every number is ___.

A) 0

B) 1

C) 2

D) 5

Answer 1

Hint: For solving this problem, we use the definition of factors of a number. A factor of a number is defined as the algebraic expression that divides any given number evenly, with its remainder being zero. In other words, it is also known as the product of multiple factors. Using this definition, we will figure out the number which is a factor of every number.

Complete step-by-step solution:

As we know Factors are all the numbers that divide a number completely, i.e., without leaving any remainder, are called factors of that number. 

Multiples are those numbers which on multiplication give the desired number. All these multiples individually can be named as a factor of the given number. 

To find the factors of any given number, we express each number as a product of prime numbers since they do not leave any remainder. 

For example, consider some numbers such as 1, 8, 21, 29.

The factor of 1 is 1. 

The factors of 8 are 1, 2, 4 and 8. 

The factors of 21 are 1, 3, 7 and 21

The factors of 29 are 1 and 29.

From the above data, we observe that 1 is the greatest factor of itself and the smallest factor of any other number.

Therefore, 1 is the factor of every number. Hence, option (B) is correct.

Note: 

• Here, $0$ is not the correct answer. Zero is not the factor of any number because if we divide a number by zero, the value is not defined.

• The largest number that divides two or more numbers is the highest common factor (HCF).