Factors of 47 with Proof and Examples

We can define factors of any number as an integer that divides another number by itself and leaves no remainder. So, if we multiply two whole numbers to produce a product, the numbers being multiplied are the factors of the result because this product is divisible by them.

For example, the integers 2 and 3 can divide the integer 6 without leaving any remainder; so, 2 and 3 are factors of 6. Factors of 47 are any integers that may be multiplied by another number to produce exactly 47. In other words, determining the factors of 47 is equivalent to breaking down the number 47 into all of the smaller components that can be put in a multiplication equation to equal 47.

Finding the Factors of 47 Using Division Method

In this section, we will learn how to find the factors of 47. There are several methods of finding the factors of an integer. Here, we will follow the Division Method. In this method, we start with 1 and check 2, 3, 4, 5, 6, 7 up to 23 (almost half of 47) to see if any numbers can divide 47 and leave zero as the remainder, then the corresponding divisor and quotient will be treated as the factors of 47.

$47 \div 1=47$, 0 remainder

$47 \div 47=1$,0 remainder

A total of two factors are there: 1 and 47.

Prime Factorisation of 47

A prime number is a positive integer that has only two factors 1 and the number itself. For example, 2, 3, 5… etc.

One of the most useful methods of finding the factors of an integer is prime factorisation. In this method, we factorise an integer only into its prime factors. 47 is a known prime number. Therefore, 47 is the only prime factor 47. This can be easily understood by the following factor tree of 47:

Prime Factorisation of 47

Factor Tree of 47

The factors of 47 are 1 and 47. This can be easily understood by the following factor tree of 47:

Factor Tree of 47

Factors of 47 in Pairs

A pair of factors of 47 will be a pair of factors $\left(f_1, f_2\right)$ of 47 whose product $f_1 f_2$ equals 47. We have

$47 = 47 \times 1$

Hence, by definition, the pair factor of 47 is (1,47).

Interesting Facts

• Prime numbers have exactly two factors: 1 and that number itself.

• Composite numbers have more than two factors.

• 1 is neither prime nor composite as it has only one factor i.e., 1, the number itself.

Solved Examples

Example 1: Find the sum of all the factors of 47.

Solution: To find the sum of all factors of 47, we need to find all the factors of 47 first. As we have discussed before, 47 has only two factors: 1 and 47.

Therefore, the sum of all the factors of 47 is (47+1)=48.

Example 2: Calculate the mean of all the factors of 47.

Solution: We are aware that 1 and 47 are the factors of 47.

In mathematics, mean is defined as the average of the provided numbers, which is determined by dividing the sum of the given numbers by the total number of terms.

$mean=\dfrac{\text{sum of terms}}{\text{Total no. of terms}}$

$mean =\dfrac{(1+47)}{2}=\dfrac{48}{2}$

The average of all the 47 factors is therefore 24.

Practice Problem

1. What is the lowest common multiple between 47 and 35?

2. What is the product of 47 factors?

Answers

1. 1645

2. 47

Conclusion

The factors of 47 can be obtained by several methods such as Division Method, Prime Factorisation Method, etc. It has a total of 2 factors: 1 and 47. The prime factorisation of 47 is 47. 47 is a prime number so its pair factor is (1,47). We hope this article helped you understand how to factor 47. Take out a pencil and piece of paper and try to practise the questions given above in this article by yourself.