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Lesson 1: Factors and multiples

# 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?

• How do you know that Something is divisible by a certain number
• There is also another rule for 11.
42 x 11 = 462
You put the number that is on the 10's place in the factor that is being multiplied by 11 (which is 4) to the hundreds place in the multiple.
The 2 in the factor's ones place goes into the multiple's ones place too.
You then add the 4 and the 2 (the digits in the factor) which equals 6; 4 + 2 = 6
The 6 then goes into the tens place of the multiple.

P.S. This can be only used for 2 digit numbers multiplying the 11.
• 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.
• 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.
• do's 2.4x 5= 12
• That is correct, because how you can figure that out without decimals is by multiplying 24x5, which is 120, then move the decimal place 2 to the left, leaving you with 12.0, or 12.
• can decimals be factor pairs?
• Factors of a number can be whole numbers, both positive and negative, but they cannot be decimals.

Hope this helps!🙂
• "To figure out if something is divisible by three, you add up its digits and if the sum is divisible by three, we're in business.". Please may you share the video where this trick relating to division by three is introduced? I forgot about it.
• what 'find all factors' of 120 mean
what to watch before this topic
whats 'factors' what da mean
• Factors are numbers that multiply to create another number. Or, you can think of factors as all numbers that divide evenly into the original number. For example: All factors of 24 are:
1, 2, 3, 4, 6, 8, 12, 24

Hope this helps.
• I noticed at he mentioned long division and I'm not very good with it so what videos should I watch to help with that?
• If you watch the videos on unit 5 lesson 6 for 4th grade there should be videos for long division, but if I remember right the videos teach you how to do it with partial products, but its basically the same thing.
• what's the divisibility rule?
• Divisibility tests from 1-10:
2: Even - ends in a 0, 2, 4, 6 or 8.
3: Sum of digits is divisible by 3 (this can be reran). Eg. 23553, 2+3+5+5+3=18, 1+8=9, divisible!
4: Last 2 digits are divisible by 4. OR, n/2 is even.
5: Ends in a 5 or 0.
6: Even and divisible by 3.
7: Double the last digit and subtract it from the rest of digits. The result is divisible by 7 (this can be reran). Eg. 231, 1*2 = 2, 23 - 2 = 21, divisible!
8: Last 3 digits are divisible by 8. OR, n/2 is divisible by 4.
9: Sum of digits is divisible by 9 (this can be reran).
10: Ends in a 0.
• i don't get it
• i am cool
(1 vote)