{"id":290,"date":"2023-02-08T09:49:28","date_gmt":"2023-02-08T09:49:28","guid":{"rendered":"https:\/\/www.matematikazavsicki.com\/en\/?p=290"},"modified":"2023-02-08T09:49:29","modified_gmt":"2023-02-08T09:49:29","slug":"divisibility-rules-of-2-3-or-6","status":"publish","type":"post","link":"https:\/\/www.matematikazavsicki.com\/en\/divisibility-rules-of-2-3-or-6\/","title":{"rendered":"Divisibility rules of 2 3 or 6"},"content":{"rendered":"\n

Here you can see examples of divisibility rules of 2, 3, or 6! For each sign, you have indicated how you can use it in a specific solved example. All divisibility rules of 2, 3, or 6 are related!<\/p>\n\n\n\n

Divisibility of 2<\/h2>\n\n\n\n

The divisibility rule of 2 is:<\/p>\n\n\n\n

Every even integer is divisible by 2 (a number ending in one of the digits 0, 2, 4, 6, or 8). A given number is not divisible by 2 if it is odd (a number ending in one of the digits (1, 3, 5, 7, or 9).<\/p>\n\n\n

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\"Divisibility<\/figure>\n<\/div>\n\n\n

Example 1: Which of the numbers 17, 22, 84 is divisible by 2?<\/p>\n\n\n\n

The number 17 is odd, so it is not divisible by 2. The numbers 22 and 84 are even, so they are divisible by 2.<\/p>\n\n\n\n

The divisibility rule of 2 is the simplest of all divisibility signs in general!<\/p>\n\n\n\n

Divisibility rule of 3<\/h2>\n\n\n\n

The divisibility rule of 3 is:<\/p>\n\n\n\n

A number is divisible by 3 if the sum of its digits is divisible by 3!<\/p>\n\n\n\n

To determine whether a given number is divisible by 3, we need to determine the sum of its digits. If this sum is divisible by 3, then that number is divisible by 3. If the sum is not divisible by 3, then the number is not divisible by 3 either.<\/p>\n\n\n

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\"Divisibility<\/figure>\n<\/div>\n\n\n

Example 2: Using the sign of divisibility by 3, determine whether the number 1854 is divisible by 3!<\/p>\n\n\n\n

First, we calculate the sum of the digits of the number 1854!<\/p>\n\n\n\n

1 + 8 + 5 + 4 = 18<\/p>\n\n\n\n

The sum of the digits of the number 1854 is 18! The sum of the digits is divisible by 3, so we conclude that the number 1854 is divisible by 3. If we try to prove it, we will get that it holds:<\/p>\n\n\n\n

1854 : 3 = 618<\/p>\n\n\n\n

which confirms that indeed the number 1854 is divisible by the number 3.<\/p>\n\n\n\n

Example 3: Using the sign of divisibility by 3, determine whether the number 7631 is divisible by 3!<\/p>\n\n\n\n

First, we calculate the sum of the digits of the number 7631!<\/p>\n\n\n\n

7 + 6 + 3 + 1 = 17<\/p>\n\n\n\n

The sum of the digits of the number 7631 is 17! The sum of the digits is not divisible by 3, so we conclude that the number 7631 is not divisible by 3.<\/p>\n\n\n\n

Divisibility Rule of 6<\/h2>\n\n\n\n

The divisibility rule of 6 is:<\/p>\n\n\n\n

A given number is divisible by the number 6 if that number is divisible by both the number 2 and the number 6!<\/p>\n\n\n\n

To determine whether a given number is divisible by the number 6, we need to separately determine whether that number is divisible by 2 and whether it is divisible by the number 3. If the given number is divisible by both numbers (divisible by both 2 and 3), then we conclude<\/a> that that number is certainly divisible by 6. If a given number is not divisible by one of the numbers 2 or 3 or is not divisible by either 2 or 3, then that number is certainly not divisible by the number 6.<\/p>\n\n\n

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\"Divisibility<\/figure>\n<\/div>\n\n\n

Example 4: Using the sign of divisibility by 6 determine whether the number 9822 is divisible by the number 6!<\/p>\n\n\n\n

First part: First we consider whether the number 9822 is divisible by the number 2.<\/p>\n\n\n\n

The number 9822 is divisible by 2 because the number 9822 is an even number!<\/p>\n\n\n\n

We continue our examination of divisibility by 3!<\/p>\n\n\n\n

Second part: We examine whether the number 9822 is divisible by the number 3.<\/p>\n\n\n\n

First, we determine the sum of the digits of the number 9822!<\/p>\n\n\n\n

9 + 8 + 2 + 2 = 21<\/p>\n\n\n\n

The sum of the digits of the number 9822 is 21. The number 21 is divisible by 3, so we conclude that the number 9822 is surely divisible by 3.<\/p>\n\n\n\n

Conclusion on divisibility by 6! The number 9822 is divisible by 2 (first part) and 3 (second part), so since it is divisible by both 2 and 3, the number 9822 is surely divisible by 6!<\/p>\n\n\n\n

If we check by division we get that:<\/p>\n\n\n\n

9822 : 6 = 1637<\/p>\n\n\n\n

which confirms that the number 9822 is indeed divisible by the number 6.<\/p>\n\n\n\n

Check the rule of divisibility of 9<\/a>!<\/p>\n\n\n\n

Examples of numbers that are not divisible by the number 6<\/h3>\n\n\n\n

Example 5: Determine if the number 7941 is divisible by the number 6!<\/p>\n\n\n\n

The number 7941 is odd, which is why it is not divisible by 2. As soon as divisibility by the number 2 is not satisfied, then the number 7941 is certainly not divisible by the number 6. In this situation, we do not need to continue with the examination of divisibility by 3.<\/p>\n\n\n\n

Example 6: Determine if the number 812 is divisible by the number 6!<\/p>\n\n\n\n

First part: First we consider whether the number 812 is divisible by 2.<\/p>\n\n\n\n

The number 812 is divisible by 2 because the number 812 is an even number!<\/p>\n\n\n\n

We continue our examination of divisibility by 3!<\/p>\n\n\n\n

Second part: We examine whether the number 812 is divisible by the number 3.<\/p>\n\n\n\n

First, we determine the sum of the digits of the number 812!<\/p>\n\n\n\n

8 + 1 + 2 = 11<\/p>\n\n\n\n

The sum of the digits of the number 812 is 11. The number 11 is not divisible by 3, so we conclude that the number 9822 is certainly not divisible by 3. Finally, the conclusion follows that the number 812 is not divisible by the number 6 because it is not divisible by 3, although we previously established that it is divisible by the number 2!<\/p>\n\n\n\n

As can be concluded, these divisibility rules of 2, 3, or 6 are related to each other!<\/p>\n\n\n\n

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