Divisibility Rules - 7 – Practice Problems

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A number is divisible by 7 if it has a remainder of zero when divided by 7. Examples of numbers which are divisible by 7 are 28, 42, 56, 63, and 98. Divisibility by 7 can be checked by using long division, although this process can be quite time-consuming. Especially when faced with a very large number. Thus, knowledge of divisibility rules for 7 can be very helpful for determining if a number is divisible by 7 or not quickly.

Here are two rules which can be utilized to test divisibility by 7:
Rule 1: Remove the last digit, double it, subtract it from the truncated original number and continue doing this until only one digit remains. If this is 0 or 7, then the original number is divisible by 7. For example, to test divisibility of 12264 by 7, we simply perform the following manipulations:
1226 - 8 = 1218
121 - 16 = 105
10 - 10 = 0
Thus, 12264 is divisible by 7.

Rule 2: Take the digits of the number in reverse order, that is, from right to left, multiplying them successively by the digits 1, 3, 2, 6, 4, 5, repeating with this sequence of multipliers as long as necessary. Then add the products. If the resulting sum is divisible by 7, then the original number is divisible by 7. For example, to test divisibility of 12264 by 7, we simply check
4(1) + 6(3) + 2(2) + 2(6) + 1(4) = 4 + 18 + 4 + 12 + 4 = 42, a two-digit number divisible by 7. Hence, 12264 must also be divisible by 7.

Gain familiarity with factors and multiples.

CCSS.MATH.CONTENT.4.OA.B.4

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Exercises in this Practice Problem
State how to use the divisibility rules of the number $7$.
Summarize the divisibility rule for $7$.
Explain how to use the divisibility rule of $7$ with large numbers.
Determine which offers are divisible by $7$.
Explain what it means if a number is divisible by another number.
Determine which numbers are divisible by $7$.