After multiplication, it is time to learn certain divisibility rules to ease our calculations. The basic rules for divisibility by 2, 3, 5, 9, 11 are fairly well known. So now we are going to learn the divisibility property for 7
First we need to know the additive osculator for 7, which is 5.
The rule for calculation:
Multiply the units digit by 5 (the osculator) and add the answer to the truncated number (remaining digits of the number). We can proceed in this way till we get a number small enough for us to decide whether the number is divisible by 7.
Let us see this with an example:
Consider 1253.
Step 1: Multiply 3 by 5 = 15
Step 2: Add 15 to the truncated number 125 = 140
Step 3: Look at 140, can you say whether it is divisible by 7?
Yes, it is. Then the given number 1253 is also divisible by 7.
That is all! Interesting?
Let us try some more examples.
1.) 3066
Step 1: 6 x 5 = 30
Step 2: 306 + 30 = 336. We cannot decide by looking at 336, so
repeat steps 1 and 2 for the number 336
Step 3: 6 x 5 = 30
Step 4: 33+ 30 = 63
We know 63 is divisible by 7
So 3066 is also divisible by 7
2.) 8637
Step 1: 7 x 5 = 35
Step 2: 863 + 35 = 898
We cannot decide by looking at 898, so we do the steps for 898
Step 3: 8 x 5 = 40
Step 4: 89 + 40 = 129
Again do the steps for 129
Step 5: 9 x 5 = 45
Step 6: 12 + 45 = 57
57 is not divisible by 7
So 8637 is not divisible by 7