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Divisibility
The document discusses rules for determining if a whole number is divisible by other whole numbers from 2 to 13. It provides the following key points: - A number is divisible by 2 if it is even. - For numbers 3-9 and 11-13, various tests are provided using digit sums or differences that must be divisible by the number in question. - A number is divisible by 10 if it ends in 0.
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Divisibility
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- 2. DEFINITION: A WHOLENUMBER DIVIDES ANOTHER IF THE REMAINDER IS ZERO, THIS WHOLE NUMBER IS SAID TO BE A DIVISOR (OR FACTOR) OF THE OTHER NUMBER OR THAT THE OTHER NUMBER IS DIVISIBLE BY THE WHOLE NUMBER.
- 3. DIVISIBILITY BY 2 Anumber is divisible by 2 if it ends in 0, 2, 4, 6, and 8. For example 118 is divisible by 2. All even numbers are divisible by 2.
- 4. DIVISIBILITY BY 3 Anumber is divisible by 3 if the sum of the digit is divisible by 3. Example 1. 2613, 2 + 6 + 1 + 3 = 12; 12 is divisible by 3, therefore 2613 is divisible by 3. 2. 4723, 4 + 7 + 2 + 3 = 16; 16 is not divisible by 3, there fore 4723 is not divisible by 3.
- 5. DIVISIBILITY BY 4 Anumber is divisible by 4 if the number formed by the last two digits is divisible by 4. Example 1. 5110, the last two digits is 10 and it is not divisible by 4, therefore the given cannot be divided by 4. 2. 2336, the last two digits 36 is divisible by 4, thus, 2336 is divisible by 4.
- 6. DIVISIBILITY BY 5 Anumber is divisible by 5 if it ends in 0 and 5 Example 1. 1050, this is divisible by 5 because it ends with 0. 2. 1212, this is not divisible by 5 because it ends with 2
- 7. DIVISIBILITY BY 6 Anumber is divisible by 6 if it is even and it is divisible by 3. Example 1. 2613, is divisible by 3 but it is not even so this is not divisible by 6. 2. 2442, is divisible by 3 and is even, therefore we can divide it by 6.
- 8. DIVISIBILITY BY 6 Anumber is divisible by 6 if it is even and it is divisible by 3. Example 1. 2613, is divisible by 3 but it is not even so this is not divisible by 6. 2. 2442, is divisible by 3 and is even, therefore we can divide it by 6.
- 9. DIVISIBILITY BY 7 Anumber is divisible by 7 if the difference between twice its ones digit and the number formed by the remaining digits is 0 or is divisible by . Example 1. 938, the ones digit is 8 and twice the ones digit that would mean 2(8) which is 16.The number remaining is 93. 93-16 = 77 and 77 is divisible by 7. 2. 153, the ones digit is 3, so it will be 2(3) = 6, the remaining number is 15. 15 - 6 = 9, and 9 is not divisible by 7, thus this is not divisible by 7.
- 10. DIVISIBILITY BY 8 Anumber is divisible by 8 if the number formed by the last three digits is divisible by 8. Example 1. 913,342; the last three digits 342 is not divisible by 8, therefor this is not divisible by 8. 2. 61,848; the last three digits 848 is divisible by 8, therefor it is divisible by 8.
- 11. DIVISIBILITY BY 9 Anumber is divisible by 9 if the sum of the digits is divisible by 9. Example 1. 2754; 2 + 7 + 5 + 4 = 18, and it is divisible by 9, therefore the given is divisible by 9. 2. 4129; 4 + 1 + 2 + 9 = 16, it is not divisible by 9, so the given is not divisible by 9.
- 12. DIVISIBILITY BY 10 Anumber is divisible by 10 if it ends in 0.
- 13. DIVISIBILITY BY 11 Anumber is divisible by 11 if the difference between the sum of the digits in the old places (starting from the rightmost digit) and the sum of the digits in the eleven places is 0 or divisible by 11. Example 1. 137,874; Odd places: 4 + 8 + 3 = 15, Even places: 7 + 7 + 1 = 15, Odd sum - Even sum (15 - 15 = 0), therefore this is divisible by 11. 2. 145,548; Odd places: 8 + 5 + 4 = 17, Even places: 4 + 5 + 1 = 10, Odd sum - Even sum (17 - 10 = 7), therefore this is not divisible by 11.
- 14. DIVISIBILITY BY 13 Anumber is divisible by 13, if the sum of four times the one's digit and the number formed by the remaining digit is divisible by 13. Example 1. 116; the ones digit is 6, four times is 32, 32 + 11 = 43, the sum is not divisible by 13, therefore this is not divisible by 13. 2. 223; the ones digit is 3, four times is 12, 12 + 22 = 36, the sum is divisible by 13, therefore this is divisible by 13.
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