The divisibility rule of 7 is one of the most unknown divisibility rules in general! Probably the divisibility of all the other numbers from the top ten is much better known than the divisibility of the number 7. That is why our team has worked diligently to create a guide with several steps that can very well explain to you how the divisibility rule of 7 reads, but also how applied in solving specific examples of numbers for which we wonder if they are divisible by the number 7 or not!
Divisibility Of 7
We will explain the divisibility rule through the following few steps:
- Calculate the product of the digit (the number whose divisibility you are currently examining) in units with the number 2.
- Subtract the number obtained from the first step from the remainder of the given number without its units digit.
- If the obtained result is equal to 0 or is a number that is a multiple of the number 7, then the given number is divisible by the number 7!
The rule is not as simple as other rules for determining the divisibility of other single-digit numbers, but it is still not very difficult to understand and use in certain examples. See how the rule of divisibility by 7 is used in concrete examples below! Look at the first example:
Examples
Example 1: Determine if the number 476 is divisible by the number 7!
We start by applying the rule for determining divisibility by the number 7!
First step: The digit in the units place in the number 476 is the digit 6. We calculate the product of the digit 6 with the number 2!
6×2=12
Second step: We calculate the difference between the remainder of the number 476 without its last digit and the result of the first step!
47-12=35
Third step: We analyze the result! The number 35 is a multiple of the number seven (because 5×7=35), which is why we come to the conclusion that the number 476 is divisible by the number 7!
If you decide to use a calculator to check the accuracy of the previous task, then you will find that 476:7=68, that is, that the number 476 is indeed divisible by the number 7!
Consider the second example!
Example 2: Determine if the number 233 is divisible by the number 7!
First step: The digit in the units place in the number 233 is the digit 3. We calculate the product of the digit 3 with the number 2!
3×2=6
Second step: We calculate the difference between the remainder of the number 233 without its last digit and the result of the first step!
23-6=17
Third step: We analyze the result! The number 17 is not a multiple of the number seven, which is why we come to the conclusion that the number 233 is not divisible by the number 7! If you decide to use a calculator to check, then you will see that dividing the number 233 by the number 7 gives a decimal number, that is, the number 233 is not divisible by the number 7!
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