Factors are defined as whole numbers that are multiplied together to produce another number. If a × b = c then a and b are known to be the factors of c.
Say you wanted to find the factors of 15. You would find all pairs of numbers that when multiplied together resulted in 15. We know 3 and 5 are factors of 15 because 3 × 5 = 15. Also, 1 and 15 are factors of 15 because 1 × 15 = 15. The factors of 15 are 1, 3, 5, 15.
You can also think about factors in the terms of division: The factors of a number include all numbers that divide evenly into that number, basically leaving no remainder. Consider the number 12. Since 12 is evenly divisible by 2 and 6, you can conclude that both 2 and 6 are the factors of 12.
How to Factor Numbers?
Factors numbers are calculated by trial division. Follow these steps to use trial division to find the factors of any given number.
First, you need to find the square root of the integer number n and round down to the closest whole number. Let's call this number s.
Start with the number one and find the corresponding factor pair: n ÷ 1 = n. So 1 and n are a factor pair because division results in a whole number with zero remainders.
Do the same with the number 2 and proceed to test all integers (n ÷ 2, n ÷ 3, n ÷ 4... n ÷ s) up through the square root rounded to s. You need to record the factor pairs where division results in whole integer numbers with no remainders.
When you reach n divided s and you have recorded all factor pairs you have successfully factored the number n.
Factors of 10
The factors of 10 are the numbers that divide the original number uniformly. Factor pairs of the number 10 are the whole numbers, which when multiplied together produces the original given number.
Factors of 10 are 1, 2, 5, and 10.
In the factorization method, first consider the numbers, 1 and 10 as factors of 10 and you need to continue with finding the other pair of multiples of 10 which gives the results as the original number.
Pair Factors of 10
To find the pair factors of the number 10, multiply the two numbers in a pair to get the original number as 10, such numbers are as follows.
If 1 × 10 equals 10, then (1, 10) is a pair factor of 10.
Similarly, let us find other different pair factors of 10.
2 × 5 equals 10, (2, 5) is a pair factor of 10
Therefore, the positive pair factors of 10 are (1, 10), as well as (2, 5).
How to Find the Factors of 10?
Learn the following steps given below to find factors of 10.
First, write the number ten
Find the two numbers, which give the result as 10 under the multiplication, say 2 and 5, such that 2 × 5 equals 10.
We know that the numbers 2 and 5 are the prime number which has only two factors, i.e., 1 and the number itself. So, we cannot further factorize.
The factors of 2 are equal to 2 × 1.
The factors of 5 are equal to 5 x 1.
Therefore, the factorization of 10 is written as 10 equals 2 × 5 × 1.
Finally, write down all the unique numbers which we can obtain from 10 equals 2 × 5 × 1.
Factors of Negative Numbers
All of the above information and methods generally apply to factoring different negative numbers. Just keep in mind that you need to follow the rules of multiplying and dividing negative numbers to find all factors of any negative numbers. For example, to find the factors of -6, we write them as (1, -6), (-1, 6), (2, -3), (-2, 3).
Factors are always defined as whole numbers or integers and never decimals or fractions.
Each and every even number will have number 2 as their factor.
All numbers that end with the number 5 will have 5 as their factor.
All numbers that are greater than 0 and ending with a 0 will have numbers 2, 5, and 10 as their factors.
Algebraic expressions can often be solved or simplified through factoring.