Tests of divisibility
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This document provides simple tests and tricks for determining if a number is divisible by certain integers between 2 and 11. It explains that to check divisibility by: - 2, look at the last digit - 3, sum the digits and check if divisible by 3 - 4, check if the last two digits are divisible by 4 - 5, check if the last digit is 0 or 5 - 6, check if divisible by both 2 and 3 - 8, check if the last three digits are divisible by 8 - 9, sum the digits and check if divisible by 9 - 10, check if it ends in 0 - 11, take the difference of sums of odd and even place digits.
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Divisibility rules provide ways to determine if a number is divisible by another number without performing long division. The document outlines divisibility rules for numbers 1-10. It explains that for divisibility by 2, 4, 5, and 10 you check the last digit(s) of the number. For divisibility by 3 and 9 you sum the digits. For divisibility by 6 you check divisibility by both 2 and 3. Divisibility by 7 involves subtracting twice the last digit from the remaining digits. Divisibility by 8 checks the last three digits.Playing with numbers
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This document discusses tests for divisibility of numbers by single-digit numbers from 2 to 11. It provides examples for each divisibility rule:
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- For divisibility by 3 or 9, the sum of the digits must be divisible by that number.
- A number is divisible by 4 if the last two digits are divisible by 4.
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2) A number is divisible by 3 if the sum of its digits is divisible by 3.
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The document outlines 9 rules for determining divisibility by single digit numbers from 2 to 10. It states that a number is divisible by:
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- 5 if the last digit is 0 or 5
- 6 if it is divisible by both 2 and 3
- 7 using a "doubling and subtracting" process with the digits
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Tests of divisibility
- 1. Simple tricks and tips to solve math’s problems easily Tests of Divisibility
- 2. Tests of Divisibility With this simple short cuts you can find out a number is divisible by a given number Divisible by 2: A number is divisible by 2, if its unit’s digit is any of 0, 2, 4, 6, 8. Example: 6798512 Divisible by 3: A number is divisible by 3, if sum of its digits divisible by 3. Example : 123456 1+2+3+4+5+6 = 21 21 is divisible by 3 so 123456 is also divisible by 3
- 3. Divisible by 4: if the last two digits of a given are divisible 4, so the number can be divisible by 4. Example : 749232 Last two digits are 32 which are divisible by 4 so the given number is also divisible by 4 Divisible by 5: If unit’s digit of a number is either ‘0’ or ‘5’ it is divisible 5. Example : 749230 Divisible by 6: If a given number is divisible by 2 and 3 (which are factors of 6), then the number is divisible by 6. Example : 35256 Unit’s digit is 6 so divisible by 2 3+5+2+5+6 = 21 so divisible by 3 So 35256 divisible by 6
- 4. Divisible by 8: if last 3 digits of a given number is divisible 8, then the given number is divisible 8. Example: 953360 360 is divisible by 8, so 953360 is divisible by 8 Divisible by 9: A number is divisible by 9, if sum of its digits divisible by 9. Example : 50832 5+0+8+3+2 = 18 divisible by 9 so 50832 divisible by 9 Divisible by 10: A number is divisible 10, if it ends with 0. Example : 508320
- 5. Divisible by 11: A number is divisible by 11,if the difference of sum of its digits at odd places and sum of its digits at even places , is either 0 or a number divisible by 11. Example : 4832718 (sum of digits at odd places ) – (sum of digits at even places) =(8+7+3+4)-(1+2+8) = 11 which is divisible by 11. So 4832718 is divisible by 11. Simple tricks, which very helpful to solve math’s homework problems easily