Question

How do you list all the factors of $40$ from least to greatest?

Answer 1

Hint: Here, we have to list all the factors of $40$ from least to greatest. Factors can be defined as the pair of numbers which when multiplied gives the original number and also defined as the number which on dividing the original number gives us a quotient as a whole number. So, here we will find the numbers that divide $40$ and give us a quotient as a whole number and we will take the numbers from least to greatest.

Complete step by step answer:
Factors can be defined as the pair of numbers which when multiplied gives the original number and also defined as the number which on dividing the original number gives us a quotient as a whole number. The factors can be positive numbers or negative numbers.There are various methods to find the factors such as factorization method, prime factorization method, division method and divisibility method.

So, now we find the numbers which divide $40$ and give us the quotient as a whole number and remainder as $0$.Now, let us check the divisibility of $40$.
$ \Rightarrow 40 \div 1 = 40$
$40$ is divisible by $1$. So, $1$ is a factor of $40$.
$ \Rightarrow 40 \div 2 = 20$
$40$ is divisible by $2$. So, $2$ is a factor of $40$.
$ \Rightarrow 40 \div 4 = 10$
$40$ is divisible by $4$. So, $4$ is a factor of $40$.
$ \Rightarrow 40 \div 5 = 8$
$40$ is divisible by $5$. So, $5$ is a factor of $40$.
$ \Rightarrow 40 \div 8 = 5$

$40$ is divisible by $8$. So, $8$ is a factor of $40$.
$ \Rightarrow 40 \div 10 = 4$
$40$ is divisible by $10$. So, $10$ is a factor of $40$.
$ \Rightarrow 40 \div 20 = 2$
$40$ is divisible by $20$. So, $20$ is a factor of $40$.
$ \Rightarrow 40 \div 40 = 1$
$40$ is divisible by $40$. So, $40$ is a factor of $40$.
Therefore, the factors of $40$ are $1,2,4,5,8,10,20,40$. The least factor of $40$ is $1$ and the greatest factor of $40$ is $40$.

Therefore, the list of all the factors of $40$ from least to greatest is $1,2,4,5,8,10,20,40$.

Note: Factors can be defined as the number which on dividing the original number gives us a quotient as a whole number and $0$ as a remainder. Decimal numbers and fractions cannot be termed as a factor. Note that factors and multiples are not the same. The factors can be defined as the exact divisors for the given number on the other hand multiples are defined as the numbers which are obtained when multiplied by the other numbers. The number of factors are finite but the number of multiples are infinite.