Math Tricks: How to Check Divisibility in 5 Seconds (No Calculator Needed!)

[00:00:00]Let's unlock the secrets of divisibility tests.

[00:00:04]When we say a number is divisible by another, it simply means you can divide them without any remainder left over.

[00:00:11]For example, 16 / 8 is exactly 2. No leftovers. And the best part? You can use clever math tricks to test this without doing any long division. Let's look at the most common tests for the numbers 2, 3, 5, and 11. First, divisibility by 2.

[00:00:31]This one is easy. Any number ending in an even digit, like 2, 4, 6, 8, or 0, is divisible by 2.

[00:00:40]If it ends in an odd digit, it is not.

[00:00:43]Next, divisibility by 3.

[00:00:46]Here, we use the digital root. Just add up all the digits of the number. If the sum is 3, 6, or 9, it is divisible by 3.

[00:00:56]If the sum still has more than one digit, just keep adding those digits together until you get a single digit.

[00:01:03]Third, divisibility by 5. Super simple.

[00:01:07]If a number ends in a 5 or a 0, it is perfectly divisible by 5.

[00:01:12]Any other ending digit means it is not.

[00:01:15]Finally, the trick for 11. Alternately, place plus and minus signs in front of each digit, always starting with a plus for the first number, and calculate the result. If the final answer is 0 or a multiple of 11, then the original number is divisible by 11. Now that we know the rules, let's put them to the test with a real example. Let's put those rules to the test.

[00:01:40]Which of the following numbers are divisible by 3?

[00:01:46]Remember the rule for 3. Add the digits to find the digital root. If that root is 3, 6, or 9, the number is divisible by 3.

[00:01:58]Let's check option A, 31.

[00:02:01]3 + 1 = 4.

[00:02:04]Since four is not divisible by three, the answer is no.

[00:02:10]Next, option B, 54.

[00:02:13]5 + 4 = 9. 9 is a multiple of three, so yes, it is perfectly divisible.

[00:02:22]Now for option C, 768.

[00:02:25]7 + 6 + 8 = 21.

[00:02:29]Since 21 is still two digits, we add them again. 2 + 1 = 3. Yes, it is divisible by three.

[00:02:40]Finally, option D, 2,809.

[00:02:44]2 + 8 + 0 + 9 = 19.

[00:02:49]1 + 9 is 10, and 1 + 0 is 1.

[00:02:53]The digital root is one, so the answer is no.

[00:02:56]Let's look at another example.

[00:02:59]Which of the following numbers are divisible by 11?

[00:03:04]Remember the rule for 11. Alternately, place plus and minus signs in front of each digit, always starting with a plus, and calculate the result. If the answer is zero or a multiple of 11, it is divisible.

[00:03:21]Let's check option A, 71. + 7 - 1 = 6.

[00:03:27]Since six is not a multiple of 11, the answer is no.

[00:03:33]Next, option B, 154.

[00:03:37]+ 1 - 5 + 4 = 0.

[00:03:40]Since the result is zero, yes, it is perfectly divisible by 11.

[00:03:47]Now for option C, 528.

[00:03:51]+ 5 - 2 + 8 = 11.

[00:03:55]11 is a multiple of 11, so yes, it is divisible.

[00:04:00]Finally, option D, 28,094.

[00:04:04]Plus two minus eight plus zero minus nine plus four equals negative 11.

[00:04:11]Since negative 11 is a multiple of 11, the answer is yes.

[00:04:17]Mastering this alternating sign trick makes even the largest numbers easy to handle.

[00:04:23]It is homework time. Let's see how well you have mastered these divisibility tests. Question one, which of the following numbers are divisible by three?

[00:04:34]Question two, which of the following numbers are divisible by 11?

[00:04:39]Pause the video right now, grab your pen, and try to solve them using the tricks we just learned.

[00:04:44]Drop your answers in the comment section below and let us see if you can get a perfect score.