• Exponent
• Roman Numerals
• Divisibility Rules
• Factors
• Factorial
• LCM
• GCF
• Modular Arithmetic
• Scientific Notations

---

Tests for divisibility

Tests for divisibility by 2

If a number has any of the digits 0, 2, 4, 6, 8 in its units place, then that number is divisible by 2.

Simple Example

let’s say the number 3456
The number 3456 has 6 in its unit place. So that 3456 number is divisible by 2.

---

Medium Example:

---

Tests for divisibility by 3

If the sum of digits of number is divisible by 3 then the number is divisible by 3.

Simple Example

let’s say the number 3456.
The sum of the digits in the number 3456 is 3+4+5+6= 18. 18 is divisible by 3.
Hence, 3456 is divisible by 3.

---

Advance Example:

---

Tests for divisibility by 4

If the number formed by digits in the tens and units places is divisible by 4, then that number is also divisible by 4.

Simple Example

let’s say the number 3112
In the number 3112, the number formed by the digits in the tens and unit places is 12.
The number 12 is divisible by 4 so that, the number 3112 is divisible by 4.

---

Advance Example

---

Tests for divisibility by 5

If a number has either 0 or 5 in its units place, then that number is divisible by 5.

Simple Example

let’s say the number 3035.
The number 3035 has 5 in its unit place. So that 3035 is divisible by 5.

---

Tests for divisibility by 6

If a number can be divided by the numbers 2 as well as 3, then that number is divisible by 6.

Simple Example

1. let’s say the number 55128
The number 55128 has 8 in the unit place. There it is divisible by 2. The sum of the digits in the number 55128 is 5+5+1+2+8 = 21. 21 is divisible by 3. Therefore, 55128 is divisible by 6.

2. let’s say the number 45120.
The number 45120 has 0 in the unit place. There it is divisible by 2. The sum of the digits in the number 45120 is 4+5+1+2+0= 12. 12 is divisible by 3. Therefore, 45120 is divisible by 6.

---

Tests for divisibility by 9

If the sum of the digits in a number is divisible by 9, then that number is divisible by 9.

Simple Example

let’s say the number 55008.
The sum of the digits in the number 55008 is 5+5+0+0+8= 18. 18 is divisible by 9. Therefore, 55008 is divisible by 9.

---

Medium Example:

let’s say the number 2247.
The sum of the digits in the number 2247 is 2+2+4+7= 15. 15 is not divisible by 9. Therefore, 2247 is not divisible by 9.

---

Tests for divisibility by 10

If a number has 0 in its units place, then that number is divisible by 10.

Simple Example

let’s say the number 3050.
The number 3050 has 0 in its unit place. So that 3050 is divisible by 10.

---

Tests for divisibility by 11

If the difference between the sums obtained by adding alternate digits of the number is 0 or is divisible by 11 then that number is also divisible by 11.

Simple Example

let’s say the number 1463.
The sums of the alternate digits of the number 1463 are 1+6= 7 and 4+3= 7. the difference between them is 7-7= 0. Therefore, 1463 is also divisible by 11.

---

Medium Example:

let’s say the number 8243
The sums of the alternate digits of the number 8243 are 8+4= 12 and 2+3= 5. The difference between them is 12-5= 7. 7 is not divisible by 11.Therefore, 8243 is not divisible by 11.

---

Divisors of number.

The quotients obtained by dividing the number are the Divisors of number.
 To find divisor of 15, divide 15 by 3.
 We get 5 as quotients.
 So that, 3 and 5 is the divisor of 15.

Note:

•  Every number is divisible by number 1 and itself.

Simple Example

---

Medium Example:

---

Advance Example:

---

• Addition
• Subtraction
• Multiplication
• Division
• Integers
• Natural numbers
• Even odd