Difference between revisions of "Divisibility"

Revision as of 19:53, 12 August 2020

Divisibility is the ability of a number to be evenly divided by another number. For example, four divided by two is equal to two, an integer, and therefore we say four is divisible by two.

Divisibility Videos

https://youtu.be/bIipw2XSMgU https://youtu.be/6xNkyDgIhEE?t=1699

Notation

We commonly write $n|k$ . This means that $n$ is a divisor of $k$ . So for the example above, we would write 2|4.

@@ Line 1: / Line 1: @@
-== Description ==
+'''Divisibility''' is the ability of a number to be evenly divided by another number.  For example, four divided by two is equal to two, an [[integer]], and therefore we say four ''is divisible by'' two.
-Divisibility is the ability of a number to be evenly divided by another number.  For example, four divided by two is equal to two, and therefore, four is divisible by two.
+==Divisibility Videos==
+https://youtu.be/bIipw2XSMgU
+https://youtu.be/6xNkyDgIhEE?t=1699
 == Notation ==
-We commonly write <math>n|k</math>. This means that n is a divisor of k. So for the example above, we would write 2|4.
+We commonly write <math>n|k</math>. This means that <math>n</math> is a [[divisor]] of <math>k</math>. So for the example above, we would write 2|4.
-==Rules for common divisors==
-=== By <math>2^n</math> ===
-A number is divisible by <math>2^n</math> if the last <math>{n}</math> digits of the number are divisible by <math>2^n</math>.
-=== By 3 ===
-A number is divisible by 3 if the sum of its digits is divisible by 3.
-===By <math>5^n</math> ===
-A number is divisible by <math>5^n</math> if the last n digits are divisible by that power of 5.
-=== By 9 ===
-A number is divisible by 9 if the sum of its digits is divisible by 9.
-=== By 7 ===
-Rule 1:  Partition <math>n</math> into 3 digit numbers from the right (<math>d_3d_2d_1,d_6d_5d_4,\dots</math>).  If the alternating sum (<math>d_3d_2d_1 - d_6d_5d_4 + d_9d_8d_7 - \dots</math>) is divisible by 7 then the number is divisible by 7.<br>
-<br>
-Rule 2:  Truncate the last digit of <math>{n}</math>, and subtract twice that digit from the remaining number.  If the result is divisible by 7, then the number is divisible by 7.  This process can be repeated for large numbers.<br>
-=== By 11 ===
-A number is divisible by 11 if the alternating sum of the digits is divisible by 11.
-=== By 13 ===
+== See also ==
-See rule 1 for divisibility by 7, a number is divisible by 13 if the same specified sum is divisible by 13.
+* [[Divisor]]
+* [[Divisibility rules]]
+* [[Number theory]]

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Difference between revisions of "Divisibility"

Revision as of 19:53, 12 August 2020

Divisibility Videos

Notation

See also