Egiptian Number System

History of mathematics

How to read numbers in English

Divisibility Criteria

Mathematics (Bilingual)

2º ESO (UNIT 1)

Divisibility Criteria:

Divisible by 2

A number is divisible by 2 if the last digit is 0, 2, 4, 6 or 8.

Example: 2 346 is divisible by 2 because the last digit is 6.

Divisible by 3

A number is divisible by 3 if the sum of the digits is divisible by 3.

Example: 23 457 is divisible by 3 because the sum of the digits is 21 (2+3+4+5+7=21), and 21 is

divisible by 3.

Divisible by 4

A number is divisible by 4 if the number formed by the last two digits is either 00 or divisible by 4.

Example: 24 516 is divisible by 4 because 16 is divisible by 4.

Divisible by 5

A number is divisible by 5 if the last digit is either 0 or 5.

Example: 9 876 345 is divisible by 5 because the last digit is 5.

Divisible by 6

A number is divisible by 6 if it is divisible by 2 (the last digit is 0, 2, 4, 6 or 8) and it is also

divisible by 3 (the sum of the digits is divisible by 3)

Example: 534 is divisible by 6 because is divisible by 2 (the last digit is 4) and it is divisible by 3 (the sum of the digits 5+3+4=12 is divisible by 3)

Divisible by 10

A number is divisible by 10 if the last digit is 0.

Example: 12 345 890 is divisible by 10 because the last digit is 0.

Divisible by 11

To check if a number is divisible by 11, sum the digits in the odd positions counting from the left (the first, the third, …) and then sum the remainder digits. If the difference between the sums is either 0 or divisible by 11, then so is the original number.

Examples: 145 879 635 918 291

Digits in odd positions: 1+5+7+6+5=24 Digits in odd positions: 9+8+9=26

Digits in even positions: 4+8+9+3=24 Digits in even positions: 1+2+1=4

The difference is 24-24=0 The difference: 26-4=22

So 145 879 635 is divisible by 11. So 918 291 is divisible by 11.