The divisibility rule of 7 states that for a number to be divisible by 7, the last digit of the given number should be multiplied by 2 and then subtracted with the rest of the number leaving the last digit. If the difference is 0 or a multiple of 7, then it is divisible by 7. The 'Divisibility rule' or ' Divisibility test of 7' helps us to check if a number is completely divisible by 7 without actually doing the division. Let us learn more about the divisibility rule of 7 in this article. Show
What is the Divisibility Rule of 7?The divisibility rule of 7 helps us to check if a number can be completely divided by 7 without any remainder. Divisibility means checking if a number is divisible by another number without actually dividing the number. Usually, we perform the division arithmetic operation to know this. However, the divisibility rule of 7 has a shortcut method to find if a number is divisible by 7. The divisibility rule of 7 picks the last digit of a number, multiplies it by 2, and subtracts it with the rest of the number to its left. We check to see if the difference is a 0 or a multiple of 7 to confirm that it is completely divisible by 7. Let us now learn how to check if a number is divisible by 7. As we have already discussed, a number is perfectly divisible by another number if it does not leave any remainder and a quotient is a whole number. The same rule applies to the divisibility by 7. Observe the following figure to learn the divisibility rules for 7. Divisibility Rule of 7 For Large NumbersIt is easy to check the divisibility rule of 7 for smaller numbers. However, for larger numbers, we perform the divisibility test of 7. In the case of larger numbers, we repeat the process of applying the divisibility test again and again until we are sure that the number is divisible by 7.
Observe the following figure to check if 2455 is divisible by 7. From the figure, we conclude that 2455 is not divisible by 7. The same rules can be applied for numbers with more than 4-digits also. Divisibility Rule of 7 and 11The divisibility rule of 7 states that if we need to check the divisibility of a number by 7, we need to multiply the last digit of that particular number by 2, and then the product is subtracted from the rest of the number. If the difference is 0 or a multiple of 7, then we say that the given number is divisible by 7. However, the divisibility rule of 11 is different from this, According to the divisibility rule of 11, if the difference of the sum of the digits at odd places and the sum of the digits at even places of the number is 0 or divisible by 11, then the given number is also divisible by 11. For example, in 9780, if we take the digits on the odd places, we get 9 and 8 and the digits at the even places are 7 and 0. Now, 9 + 8 = 17, and 7 + 0 = 7. After finding the difference of these sums, we get 17 - 7 = 10, which is neither 0 nor divisible by 11. Therefore, we can say that 9780 is not divisible by 11. Divisibility Rule of 7 and 13Divisibility rules help us to check if a number is completely divisible by another number without actually doing the division. The divisibility rules of 7 and 13 are different. As per the divisibility rule of 7, the last digit is multiplied by 2, and the product is subtracted from the rest of the number. If the difference is 0 or a multiple of 7, then we say that the given number is divisible by 7. There are four methods by which we check the divisibility of a number by 13. Here, let us discuss one of these methods. As per one of the divisibility rules of 13, we multiply the last digit by 4, and add the product to the rest of the number. If the sum is a multiple of 13, then the number is divisible by 13. If the number is large, we repeat the same process again. Let us understand this with an example. Let us check if the number 442 is divisible by 7 and 13.
Here, we observe that 442 is NOT divisible by 7 but divisible by 13. Divisibility Rule of 7 and 8The divisibility rules of 7 and 8 are different. The divisibility rule of 7 states that the digit at the units place should be multiplied by 2, then the product needs to be subtracted from the rest of the number. If this difference results in a 0 or a multiple of 7, then the number is said to be divisible by 7. For a number to be divisible by 8, we check if the last three digits can be divided by 8 without leaving a remainder or the last three digits are 0. Let us work out the divisibility rule of 7 and 8 for the number 742.
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FAQs on Divisibility Rule of 7As per the divisibility rule of 7, the last digit of the given number is multiplied by 2, and the product is subtracted from the rest of the number. If the difference is 0 or a multiple of 7, then we say that the given number is divisible by 7. If we are not sure whether the resulting number is divisible by 7 or not, we repeat the same process with the resultant number. For example, in the number 154, let us multiply the last digit 4 by 2, which is 4 × 2 = 8. On subtracting 8 from 15, we get 7. 7 is divisible by 7 as it is the first multiple. Therefore, 154 is divisible by 7. Using the Divisibility Rule of 7, Check if 145 is Divisible by 7.By the divisibility rule of 7, the last digit should be multiplied by 2 and then subtracted with the rest of the number leaving the last digit. If the difference is 0 or a multiple of 7, then it is divisible by 7. For the given number 145, when we multiply the last digit 5 by 2, we get, 5 × 2 = 10. Now, on subtracting 10 from 14, we get 4. Since 4 is not a multiple of 7, we can conclude that 145 is not divisible by 7. What is the Divisibility Rule of 7 and 11?The divisibility rule of 7 tells us to pick the last digit of a number, multiply it by 2, and subtract the product from the rest of the number to its left. If the difference is 0 or a multiple of 7, then the given number is divisible by 7. According to the divisibility rule of 11, a number is divisible by 11 if the difference of the sum of the digits at the odd positions and even positions are either equal to 0 or a multiple of 11. In other words, the difference should be 0 or a number that 11 divides completely without leaving a remainder. How do you know if a Large Number is Divisible by 7?To know if a large number is divisible by 7 or not, we need to check the following conditions:
How Many Numbers are there Between 1 and 100 which are Exactly Divisible by 7?There are 14 numbers between 1 and 100 that are exactly divisible by 7. They are, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, and 98. What is the Divisibility Rule of 7 with Example?The divisibility rule of 7 states that if we need to check the divisibility of a number by 7, we need to multiply the last digit of that particular number by 2, and then the product is subtracted from the rest of the number. If the difference is 0 or a multiple of 7, then we say that the given number is divisible by 7. For example, let us take the number 161. So, we will multiply the last digit of 161 by 2, this means 1 × 2 = 2. Then, we will subtract this product from 16, that is, 16 - 2 = 14. And we know that 14 is divisible by 7. This means the number 161 is divisible by 7. |