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### Course: Class 6 (Old)>Unit 3

Lesson 3: Tests for divisibility

# Recognizing divisibility

Recognizing Divisibility. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Is zero a even number
• Here's a video explaining why zero is even http://www.youtube.com/watch?v=8t1TC-5OLdM
• Why does the problem skip the numbers 7 and 8? Is it like.... unsolvable?
• no its solvable but just more complex. seven being erase the final digit multiply it by five and add it to the rest and for eight you look at the last three digits which will become too big to recognize.
• So the reason we only look at the last two digits for divisibility by 4 is because they represent values that are less than 100? Because every other place value is a multiple of 100 which are divisible by 4?

Like 370 is 300 + 70. It's 3 hundreds, 7 tens and 0 ones.

300 = 100 + 100 + 100

100 / 4 = 25

So 300 / 4 = 25 * 3 = 75

But 70 is < 100

Is 70 divisible by 4?

If yes, then 370 is also divisible by 4!
Else, if no, then 370 is neither divisible by 4!

That's it?

So it needs to be divisible by 2 twice?! Or 2 to the second power. But we can't use the divisibility test for 2 alone, twice. Because that would loose the purpose of the test, because we would have to divide by 2 first, if divisible by 2, and THEN test for divisibility by 2, and then divide by 2 a second time, if divisible by 2.

So to be divisible by 8 it would need to be divisible by 2 three times!? Or 2 to the third power! But again, that looses the purpose of the test. So to really test it, you need to look at the LAST THREE digits in the number?

Like 4560 is 4000 + 560.

If we test last two digits only, like before, the test will fail.

60 divisible by 8? No!

60 / 8 = 7.5

But that does NOT mean 4560 is NOT divisible by 8!

You have to test for 560! One digit or place value more than for testing with 4!

Is 560 divisible by 8?

560 / 8 = 70

Yes!

So if 560 is divisible by 8, then so is 4560!

Because 4000 is a multiple of 1000.
And 1000 is a multiple of 100.
And we have already established that 100 is divisible by 4.
Then so is 1000 and 4000.

4000 = 1000 + 1000 + 1000 + 1000

But 570 is NOT a multiple of 1000!

570 < 1000

That's why we test it for divisibility by 8.

Am I getting this right?
• are these rules almost the same as the rules in "Divisibility Test" video?
• It was like the divisibility test. The question was is 730,397. was divisible by 2. No. Unless we were using decimal. Then the answer would be 365,198.50
• why did sal skip 7 and 8.
• i told you like 10 times
(1 vote)
• Wait so is 8 and 7 divisible by 380?
• no its not check it
• Divisibility?What's Divisibility?
• Basically when we test divisibility we want to know if a number if divisible by another number without leaving any remainder.

So for example 6 = 3 x 2 so we can say 6 is divisible by 2 and 6 is also divisible by 3.

This means when we divide 6 by 2 there is no remainder left over. And the same is true if we divide 6 by 3 leaving no remainder.

There are a whole bunch of rules to test divisibility. The easiest rule is that all even numbers are divisible by 2.

Once you are comfortable with that then its worth looking into other divisibility tests for divisibility by 3, 5 and 10. Then we can look at 4 and 6 and 8.
• Is there a reason 7 and 8 are not taught? I'm watching these videos to learn how to effectively teach students (currently in my last year of undergrad). Thank you!
• because they are more difficult than the others. As mentioned elsewhere the divisibility test for 7 is to take the last digit double it and subtract it from the remaining number. If the answer is divisible by seven the whole number is.

For eight you need to check if the last three digits are divisible by eight.

These tests are more difficult to use and aren't as applicable as the previous tests as larger numbers are required.
• Isn't it also true that any number divisible by 2 would also be divisible by 4? If this is true, why is it necessary to have a rule specific to the number 4? Also, is it true that an odd number will never be divisible by an even number?