Factors are whole numbers which are multiplied to get another whole number. It can also be defined as the multiplication of numbers to get another number. Ex: Factors for 8 are 2 and 4 as 2 × 4 = 8. Similarly, factors for 10 are 1 and 10 or 2 and 5 as 1 x 10 = 10 and 2 x 5 = 10.
1. It is essential to know that there are many numbers which have more than a single factorization or it has many factors. Ex: 16 can be factored as 1×16, 2×8 or 4×4.
2. When a number has only 1 factor it is called as a prime number. Ex: 2, 3,5,7,11,13, etc.
3. 1 is not included in factorizations as it is present in every number factorization.
4.-ve numbers can also be factors as multiplying two negatives makes a positive. Ex: Factors of 12 can be -6 and -2 or -4 and-3 or -1 and -12 apart from the other positive integers.
5. Factors in Algebra are shown using expressions. Ex: u+3. Expression y2+4y+3 has (y+3)(y+1) as factors.
The factors for a number can be found in two ways:
Division: This method is used when you want to know whether a number that you have chosen is a factor of the other number or not. If the number you have chosen is divided and gives no remainder then it is called as the factor of that number.
Ex: 15. To find if 3 is a factor of 15 or not. 15/3 = 5. Since the remainder is 0, 3 is a factor of 15.
Ex2: 6 is a factor of 26. 26/6 has a remainder of 2 hence not a factor of 26.
Factor Tree: This is a diagrammatic way to find factors for a number. First two numbers are found whose product gives the number to be factored. Ex: 24. The factors 6 and 4 gives 24. After that, use the same method to get factors for 6 and 4 and note them down, repeat the method till you get no factors for these two numbers. It is a good way to find all the factors possible for a number.
Real-life Application of Factors
A division into equal parts: Factors are necessary if you have to divide something into equal parts. Ex; there are 4 kids and there are 8 chocolates, for everyone to get equal share dividing 8 by 4 results in 2, so each kid gets 2 chocolates.
Dealing with Money: Exchanging money is an application of factors in real-life. A $50 note can be exchanged for either 4*$5 notes or 2*$20 notes and 2*$5 notes.
Time: It is another real-life application of factors. If your doctor asks you to take pills thrice a day. You will take 24/3 = 8. So you have to take it after every 8 hours.
Travel: Factors can be used in travel too. If you have to cover 600 miles, to know how much time you will spend driving if you drive at a speed of 100 mph, then it will take 6 hours to reach the destination.
Factors are an essential part of mathematics that we use day in and day out, sometimes even without realizing it! Having at least the basic knowledge in it will help you in a great way!