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# Finding factors of a number

Sal finds the factors of 120. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• You mentioned the "divisibility rule" a number of times in this video. Is there a video that teaches that, if not,where can I find the divisibility rules? • How do you know that Something is divisible by a certain number • 1 - any whole number is divisible by 1.
2 - any even number is divisible by 2.
3 - are the sum of the digits divisible by 3?
4 - is the sum of the last two digits divisible by 4?
5 - is the last digit a 5 or a 0?
6 - any number divisible by 2 & 3 is divisible by 6.
7 - is the double of the last digit subtracted from the remaining digits a multiple of 7 (or 0)?
8 - is the sum of the last three digits divisible by 8?
9 - is the sum of all the digits divisible by 9?
10 - any number that ends in 0 is divisible by 10.
11 - ???
12 - any number divisible by 4 & 3 is divisible by 12.
• So if you can "test" 6 by checking 2 and 3, can you test 8 by checking 2 and 4? •   Unfortunately not. For instance, 12 is divisible by 2 and 4, but that doesn't mean that it's divisible by 8.
• • How does one know when they have found the appropriate factors? How do you know when to stop checking? • • • I don't get the system behind this "divisibility test..." Unless I wanted to complicate things, I can't for the love of god think of a reason to use it :/

If 120 is divisible by 2 and 3, it is divisible by 6, but why doesn't this method work for divisibility by 8 or 9? Basically, is there a simple set of rules to quickly discover if a number is divisible by another number?

Right now, it just looks a lot more confusing than simply doing the full calculations... If anyone can explain the simplicity behind this I would be very thankful. • I agree that right now the divisibility test seems unnecessarily complicated right now, but I can promise you that it will become extremely important with more complicated math such as simplifying square roots, prime factorization, gcf, quadratic factoring and many other fields (as prime factorization, simplifying square roots, gcf and quadratic factoring are also necessary for other topics).

Also for the simplicity of it, you just have to memorize the ways divisibility rules (there may be a simpler way but I haven't heard of one), and if you keep practicing eventually it becomes natural and simple to perform. I can promise you that if you properly learn divisibility to rules it will be extremely helpful to you as you perform more complex math.

For now I think you should remember that:
Divisibility by 1: Every number is divisible by .
Divisibility by 2: The number should have or as the units digit.
Divisibility by 3: The sum of digits of the number must be divisible by .
Divisibility by 4: The number formed by the tens and units digit of the number must be divisible by .
Divisibility by 5: The number should have or as the units digit.
Divisibility by 6: The number should be divisible by both and .
Divisibility by 7: The absolute difference between twice the units digit and the number formed by the rest of the digits must be divisible by (this process can be repeated for many times until we arrive at a sufficiently small number).
Divisibility by 8: The number formed by the hundreds, tens and units digit of the number must be divisible by .
Divisibility by 9: The sum of digits of the number must be divisible by .
Divisibility by 10: The number should have as the units digit.
Divisibility by 11: The absolute difference between the sum of alternate pairs of digits must be divisible by .
Divisibility by 12: The number should be divisible by both and .
Divisibility by 13: The sum of four times the units digits with the number formed by the rest of the digits must be divisible by (this process can be repeated for many times until we arrive at a sufficiently small number).
Divisibility by 25: The number formed by the tens and units digit of the number must be divisible by
The divisibility rules were complied by brilliant.org and if you want the the proof of them you can check them out at this link: https://brilliant.org/wiki/proof-of-divisibility-rules/

Just remember that even though divisibility rules don't seem helpful right now, there is a point to learning them and they will be useful in the future.
• • Why are numbers that when multiplied by a fraction not considered factors?

For example:

Is 4 a factor of 6?

4 x 3/2 = 12/2
12/2 = 6 