<p> Divisibility Rules</p><p>There are several methods for testing the divisibility of a number without actually performing the division.</p><p>A Number can be divisible by...</p><p>2 If the last digit is even. 3 If the sum of the digits can be divided by 3. </p><p>4 If the last two digits can be divided by 4. </p><p>5 If the last digit is 5 or 0. </p><p>6 If the number can be divided by 2 and 3. If you double the one’s digit and subtract from the 7 remaining digits and the result is divisible by 7 or is 0. Repeat as needed. 8 If the last three digits can be divided by 8. </p><p>9 If the sum of the digits can be divided by 9. </p><p>10 If the last digit is 0. If the difference between sum of odd digits and sum 11 of even digits is divisible by 11 or is 0. Repeat as needed. 12 If the number can be divided by 3 and 4.</p><p>Example for divisibility by three rule: Example for divisibility by eight rule:</p><p>31,028,421 Add the digits: 4,973,816 Look at last three digits 3 + 1 + 0 + 2 + 8 + 4 + 2 + 1 = 21 816 21 is divisible by 3 816 / 8 = 102 (divisible by eight)</p><p>Therefore 31,028,421 is divisible by 3 Therefore 4,973,816 is divisible by 8</p><p>Example for divisibility by seven rule: Example for divisibility by eleven rule:</p><p>31,941 3194 – 2(1) = 3192 (repeat) 692,351 6 + 2 + 5 = 13 (sum even digits) 319 – 2(2) = 315 (repeat) 9 + 3 + 1 = 13 (sum odd digits) 31 – 2(5) = 21 (repeat) 13 – 13 = 0 (difference) 2 – 2(1) = 0</p><p>Therefore 31,941 is divisible by 7 Therefore 692,351 is divisible by 11</p>