This website provides free information and other free resources relating to the subject of mathematical factoring and number factors.
Mathematical factoring is the process of breaking numbers down (factoring them) into all of their component numbers or factors. Every number will have at least four factors (2 pairs). The first pair are 1 and the number itself (6 is used as an example), the second pair are -1 and the number with its opposite sign i.e. -6 in this example.
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A factor is any number that will divide into another number exactly (with no part left over) e.g. 6 can be divided by 2 (the factor in this example) 3 times. However, in total the number 6 has several factors: 1, 6, -1, -6, 2, 3, -2 and -3.
Lets assume that you are trying to confirm if the number 2 is a factor of the
number 18 or not.
Take the 18 and divide it by the 2 (the factor), the answer is 9. As there are no digits after the decimal place (i.e. it is 7 or 5 not 7.3 or 4.44) 2 is therefore confirmed as a factor of the number 18.
The quotient (the result in the example i.e. 9) is also a factor of the number 18.
Factoring a number means taking the number apart to find its factors e.g.
16 has the factors: 1, 2, 4, 8, 16
20 has the factors: 1, 2, 4, 5, 10, 20
Multiplying two of more of these numbers together may make the original number - the numbers that are multiplied are the factors of the final number.
Factoring is a key part of algebra as it helps you to solve equations and to simplify expressions and fractions. Factoring refers to the procedure of writing a given mathematical expression as a product of two or more mathematical expressions.
Prime numbers are the numbers that are greater than 1 and has only two positive factors; 1 and itself e.g. the number 7 is only exactly divisible by 1 and 7.
The opposite of a prime number is a composite number, a composite number has more than two factors e.g. 8 can be exactly divided by 1, 2, 4 and 8.
Zero and 1 are neither prime nor composite numbers.
Prime factoring is to factor and then continue factoring a number until you can no longer reduce the factors into constituent factors any further.
For example using the number 60, the factors are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. Some of these factors can be further reduced e.g. 6 = 2 x 3. When the factors can not be factored further, you will be left with prime numbers.
You can write any composite number as a product of prime factors in the case of 60 = 2 x 2 x 3 x 5. This can be further simplified using exponents to 60 = 22 x 3 x 5. (22 just means 2 x 2 i.e. 2 to the power of 2).
After factoring a number, the greatest common factor (also known as the Greatest Common Divisor or GCD) is the largest factor that is common to two or more numbers (or algebraic terms). A common factor is a factor that will divide into both numbers equally e.g. 3 is a common factor of 6 and 12 i.e. 3 x 3 = 6 and 3 x 4 = 12.
The GCF will be the highest common factor of the two numbers. For example, the GCF of 15 and 30:
Factoring is just one aspect of mathematics that has sources of further information listed in our resources pages: Links to further Resources
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