**Divisibility Rules**

Divisibility Rules for 2,3,4,5,6,7,8,9,

By: Emma Hill

Rule for 2

If the number ends in 2,4,6,8,or 0 it can be divided by 2.

Rule for 4.

If the last two digits are a multiple of four then the number can be divided by four.

Rule for 3.

If the sum of the digits is divisible by 3,the number is also.

1. 174,974,764, The number ends with a even number therefore 174,974,764 can be divided equally by 2.

2. 549,268, The number ends with a 8,so 549,268 can be equally divided by 2.

3. 7,012, 2 can be divided by 2 therefore 7,012 can be equally divided by 2.

4. 230,098,234 The number ends with 4 and 4 can be equally divided by 2.

5. 3,980, The number ends with 0,and 0 is a multiple of 2 therefore3,980 can be equally divided by 2.

1. 1,348, 48 is a multiple of 4 therefore 1,348 is divisible by 4.

2. 27,616, 16 is a multiple of 4 therefore 27,616 is divisible by 4.

3. 576,756,712, 12 is a multiple of 4 therefore 576,756,712 is divisible by 4.

4. 4,765,820, 20 is a multiple of 4 therefore 4,765,820 is divisible by 4.

5. 54,708 8 is a multiple of 4 therefore 54,708 is divisible by 4.

1.

13,210 (3+2+1+0=6) Therefore 3,210 is divisible by 3.

2.

846,555,036 (8+4+6+5+5+5+0+3+6=42) Therefore 846,555,102 is divisible by 3.

3

. 2,789,556,102 (2+7+8+9+5+5+6+1+0+2=45) Therefore 2,789,556,102 is divisible by 3.

4

. 6,903, (6+9+0+3=18) Therefore 6,903 is divisible by 3.

5

.570,999, (5+7+0+9+9+9=39) Therefore 570,999 is divisible by 3.

Rule for 5

If the last digit ends with 5 or 0.

1. 1,960, 60 can be divided by 5 so, 1,960 is divisible by 5.

2. 38,095, 5 can be divided by 5 so, 38,095 is divisible by 5.

3. 666,666,620, 0 can be divided by 5 so, 666,666,620 is divisible by 5.

4. 105, 5 can be divided by 5 so, 105 is divisible by 5.

5. 4,980 0 can be divided by 5 so, 4,980 is divisible by 5.

Rule for 6.

A number is divisible by six if it can follow the divisibility rule for 2 and 3.

1. 5,106 6 is a multiple of 2 and 5+1+0+6=12 and 12 is a multiple of 3 so 5,106 can be equally divisible by 6.

2. 636 6 is a multiple of 2 and6+3+6=15 and 15 is a multiple of 3 so 636 can be equally divided by 6.

3. 271,058 8 is a multiple of 2 and 2+7+1+0+5+8=24 and 24 is a multiple of 3 therefore 271,058 can be divided by 6.

4. 21,012 2 is a multiple of 2 and 2+1+1+2=6 and 6 is a multiple of 3 so 21,012 is divisible by 6.

5. 78,032,646 6 is a multiple of 2 and 7+8+0+3+2+6+4+6=36 and 36 is a multiple of 3 so 78,032,646 can be divided by 6.

Rule for 7.

If the last digit in the number is doubled and then subtracted from the rest of the digits.

1

. 672 (2+2=4) 67-4=63 so 672 can be divided equally by 7.

2

.357 (7+7=14) 35-14=21 therefore 357 can be divided by 7.

3

.112 (2+2=4) 11-4=7 so 112 can be divided by 7.

4

. 7,126 (6+6=12) 712-12=700 so 7,126 can be divided by 7.

5

.511 (1+1=2) 51-2=49 so 511 can be divided by 7.

Rule For 8.

If the last 3 digits are divisible by 8, so is the entire number.

1. 6008

8

is divisible by 8 so 6008 is divisible by 8.

2. 587,320

320

is divisible by 8 therefore 587,320 is divisible by 8.

3.900,096

96

is divisible by 8 therefore 900,096 can be divided equally by 7.

4. 1,024

24

is divisible by 8 so 1,024 is divisible by 8.

5. 90,088

88

is divisible by 8 therefore 90,088 is divisible by 8.

Rule for 9.

If the sum of the digits is evenly divided by 9.

1. 4,598 (4+9+5+8=27) and 27 divided by 3=9 therefore 4,598 is divisible by 9.

2. 9,999 (9+9+9+9=36) 36 divided by 4 is 9 therefore 9,999 is divisible by 9.

3. 10,006,470 (1+6+4+7=18) 18 divided by 2=9 Therefore 10,006,470 is divisible by 9.

4. 11,151 (1+1+1+5+1=9) 9 divided by 1=9 Therefore 11,151 is divisible by 9.

5. 999,999,999 (9+9+9+9+9+9+9+9+9=81) and 81 divided by 9=9 Therefore 999,999,999 is divisible by 9.

The End

Definitions

Quotient: The number obtained by dividing one quantity by another. In 45 ÷ 3 = 15, 15 is the quotient.

Divided:The amount you want to divide by.

Divisor: A number that is a factor of another number.

Remainder: The left over part in a multiplication,divsion,subtracting or adding problem.