“1, 2, and 4 are the factors of number 4. Is there any other factor?”, asked Ms. Braganza? “Other factors? We even don't know how you find these factors, and you are asking for others. It's very confusing,” children muttered.
Do you have the same issue to find the factor of any numbers? Take it easy, dear child. We have three methods for you to find the factor of any number. Let's learn one by one. But, before learning the methods, let's learn what is the factor?
Factor—Definition
A factor is any number by which another number divides completely, without leaving any remainder.
For example, 5 is the factor of 15, as it divides the number 15 completely. (Remember, 5 × 3 = 15.)
But, there could be the other factors of 15 as these numbers also divide the number 15 completely. Like, 3 is also the factor of 15 because 3 × 5 = 15.
There are three methods by which we can find the factors of any method:
Multiplication method
Division method/Factorisation method
Factor tree method
Tip: 1 and the number itself are also the factors of any number.
How to Find the Factors of 4?
Factors of 4 can be defined as the numbers that divide the original number uniformly or completely.
Find the factors of 4 by multiplication method
We know that 1 × 4 = 4,
Also, 2 × 2 = 4
and, 4 × 1 = 4
Merge all the numbers, and the result would be (1, 2, 4), it means 1, 2, 4 are factors of 4.
Interesting! Right? But can you recall any other way by which we can get 4? Your answer might be ‘No'. You are probably right. You know in Math, when you are so sure then a new possibility arises. Look below,
–1 × –4 = 4 (Remember: –1 × 4 ≠ 4, also 1 × –4 ≠ 4)
–2 × –2 = 4 (Remember: –2 × 2 ≠ 4, also 2 × –2 ≠ 4)
–4 × –1 = 4 (Remember: –4 × 1 ≠ 4, also 4 × –1 ≠ 4)
So, (–1, –4), (–2, –2) and (–4, –1) are also the factors of 4, but only in the form of pairs. These are called pair factors.
So, What are Pair Factors of 4?
To find the pair factors of the number 4, multiply the two numbers in a pair to have the original number, such numbers are as follows:
(1, 4) and (2, 2) are the positive pair factors for 4.
(-1, -4) and (-2, -2) are the negative pair factors for 4.
The Factors of 4 in Pairs
(1, 4) are the factors of 4 as 1 x 4 is equal to 4.
(2, 2) are the factors of 4 as 2 x 2 is equal to 4.
So the factors of the number 4 are 1, 2, and 4.
Prime Factors of 4 (Prime Factorization)
The prime factorization of 4 gives:
4 equals 1 x 2 x 2
Factors of 4 in Pairs:
(1 x 4)
(2 x 2)
(4 x 1)
Therefore, the prime factors of 4: 2 * 2
Find the factors of 4 by Division Method
We can use the factorization method to find the factors of 4 as well as multiples of 4. In this factorization method, we need to first consider the given number itself and one as the factors, so 4 and 1 are the factors of the number 4, and then we need to keep finding the factors of number 4 which shall give us the number 4. For that, we need to divide the number repetitively by all the small numbers or the number itself.
The division method is a basic and shortcut method to find the factor of any number. It is generally suitable for big numbers. But, how the division method performs on small numbers like 4, see below.
1 | 4 | 4 |
4 | ||
\[\rightarrow No \, remainder\] |
2 | 4 | 2 |
4 | ||
\[\rightarrow No \, remainder\] |
3 | 4 | 1 |
3 | ||
1 | \[\rightarrow remainder\] |
4 | 4 | 1 |
4 | ||
\[\rightarrow No \, remainder\] |
Therefore, 1, 2, and 4 are the factors of 4 as they are left out with no remainder.
So, What are the Factors of 4?
These are the integers that can be evenly divided into 4; they can be expressed as either individual factors or as factor pairs. In this case, we present them both ways. This is the mathematical decomposition of a particular number.
So, How Many Factors Does 4 Have?
This number has three factors: 1, 2, 4
More specifically, shown as pairs...
(1*4) (2*2) (4*1)
What is the Prime Factorization of 4?
A prime factorization is a result of factoring any given number into a set of components where every member is a prime number. This is generally written by showing 4 as a product of its prime factors. For 4, this result would be:
4 equals 2 x 2
(this is also known as the prime factorization method; the smallest prime number in this series is described as the smallest prime factor among all of them.)
Is 4 a Composite Number?
A composite number is any number that has more than 2 factors. Since, 4 has three factors, i.e., 1, 2, 4, therefore 4 is a composite number.
Is 4 a Square Number?
Yes! 4 is a square number. Its square root is an integer, specifically the number 2. –2 is also the square root of number 4.
What is the Greatest Common Factor of 4 and Another Number?
The greatest common factor (GCF) of two numbers can be determined by comparing the prime factorization or factorization of the two numbers and taking the highest common prime factor. If there is no common factor, then the GCF is equal to 1. This is also known as the highest common factor and is part of the common prime factors of two given numbers. It is the largest factor or the largest number the two numbers share as a prime factor. The least common factor or the smallest number in common of any pair of integers is the number 1.
What is a Factor Tree?
A factor tree can be defined as a graphic representation of the possible factors of numbers and their sub-factors. It is designed to simplify factorization. A factor tree is created by finding the factors of any number, then finding the factors of the number. The process continues recursively until you've derived a bunch of prime factors, this is the prime factorization of the original number. In constructing the factor tree, be sure to remember the second item in a factor pair.
How Do You Find the Factors of Any Negative Number? (eg. -4)
To find the factors of the number, let’s suppose -4, find all the positive factors (see above), and then duplicate them by adding a minus sign before each one (effectively multiplying them by -1). This addresses negative factors. (handling negative integers)
Is 4 a Whole Number?
Yes, 4 is a whole number.
Point to Remember
What are the Divisibility Rules?
Divisibility can be referred to as a given integer number being divisible for a given divisor. The divisibility rule can be defined as a shorthand system to determine what is or isn't divisible. This includes rules about even number and odd number factors.
Number | Divisibility Rule |
2 | A number is divisible by 2 if the last digit of the number is an even digit, i.e., 0, 2, 4, 6, 8. |
3 | A number is divisible by 3 if the sum of the digits is divisible by 3. |
4 | A number is divisible by 4 if the last two digits of the number are divisible by 4. |
5 | A number is divisible by 5 if the last digit of the number is either 0 or 5. |
6 | A number is divisible by 6 if the number is divisible by 2 and 3 both. |
8 | A number is divisible by 8 if the last three digits of the number are divisible by 8. |
9 | A number is divisible by 8 if the sum of the number is divisible by 9. |
10 | A number is divisible by 10 if the last digit of the number is 0. |
These divisibility rules can be used to find the factors of big numbers while using the division method.
Important Definition
The two numbers which when multiplied and given the result as the original number, can be termed as pair factors.
