Divisibility Rule for 16 Proof & Examples - How to Check Divisibility of 16?

If you want to solve problems on the divisivility rules of 16 then you can look at this page. Check whether Large Numbers are divisible by 16 or not by following the simple hacks over here. Continue to read further to study about Divisibility Rule of 16, How to Check If a Number is Divisible by 16 or not, and Solved Examples on Divisibility Test of 16, etc. Without any further delay let’s get it started.

What is the Divisibility Rule of 16?

As per the Divisibility Test of 16, a number is said to be divisible by 16 if it has an even thousands digit and the last three digits formed are divisible by 16. In case a thousand digit is odd, the number formed by the last three digits plus 8 is divisible by 16 then the number is divisible by 16.

How to Determine if a Number is Divisible by 16?

Follow the step-by-step process to identify if the given number is divisible by 16 or not. They are along the lines

• In the case of smaller numbers, you can check the divisibility of 16 by simply adding the last two digits to 4 times the rest. If the result is divisible by 16 then the number is divisible by 16.
• If the number is large and if a thousand digits are even simply look at the last three digits formed and if they are divisible by 16 the given number is divisible by 16.
• If the number is large and the thousand digit is odd add 8 to the last three digits formed and if the result is divisible by 16 given number is divisible by 16.

Solved Examples of Divisibility Rule for 16

Example 1.

Check if 133456 is divisible by 16 or not.

Solution:

Given number is 133456

Here the thousand digit is odd i.e. 3

As per the divisibility rule of 16, we will add the last three digits plus 8 = 456+8

= 464

464/16 = 29

As this result is divisible by 16 the whole number 133456 is divisible by 16.

Example 2:

See if 748 is divisible by 16 or not.

Solution:

Given number is 748

Since it is a smaller number we will see the divisibility of 16 by adding the last two digits to 4 times the rest and if it is divisible by 16 the entire number is divisible by 16.

= 4x7+48

= 28+48

= 76

76/16

As 76 doesn’t go completely in 16 the number 748 is not divisible by 16.

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What numbers are divisible by 16

List of Numbers divisible by 16: The Numbers 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304, 320, 336, 352, 368, 384, 400, 416, 432, 448, 464, 480, 496, 512, 528, 544, 560, 576, 592, 608, 624, 640, 656, 672, 688, 704, 720, 736, 752, 768, 784, 800, 816, 832, 848, 864, 880, 896, 912, 928, 944, 960, 976, 992, 1008, 1024, 1040, 1056, 1072, 1088, 1104, 1120, 1136, 1152, 1168, 1184, 1200, 1216, 1232, 1248, 1264, 1280, 1296, 1312, 1328, 1344, 1360, 1376, 1392, 1408, 1424, 1440, 1456, 1472, 1488, 1504, 1520, 1536, 1552, 1568, 1584, 1600, etc. are divisible by 16.

FAQs on Divisibility Test of 16

What is the divisibility rule for 16?

If a number has even thousands digits and the last three digits formed are divisible by 16 then the given number is divisible by 16. If a number has odd thousands digit the last three digits formed plus 8 is divisible by 16 then the given number is divisible by 16.

Is 748 divisible by 16?

Yes, 748 is divisible by 16.

What is the largest 4-digit number divisible by 16?

The largest 4-digit number divisible by 16 is 9984.

Final Words

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