Chika's Test

Chika Ofili

I've taught mathematics for 32 years this year. Unbelievable. I've taught K-12 and college. 

Every year, I am teaching one class or another the divisibility rules. The rules are important for mental math and for higher mathematics studies. They make life easier. We all know that a number ending in 0 is divisible by 10. There are rules, like that 10 divisibility rule, for all 10 digits. Except 7.  

Every year, I always teach classes that there simply is not a divisibility rule for 7, although I knew there had to be one somewhere. Maybe in higher math? I even found one once, but never used it in a class and have forgotten it. It was too algebraic for my classes and too cumbersome. 

I have wanted to take the time to figure out a 7 rule for myself. But who has the time for that? I'm pretty busy with family, bread making, insect and nature photography, reading, church . . . so if I did not need a 7 divisibility rule, I wasn't going to devise one. 

Chika Ofili, of the UK, did, though. That is his photo above, with the link to the article about his method, which is to multiply the last digit of a number by 5 and then add that sum to the remaining digits of the number: 

• Take the number 532. Its last digit is 2, so the operation prescribed is:
532 |→ 53 + (5 × 2) = 63.
Note that both 63 and 532 are multiples of 7. 
• Take the number 973. Its last digit is 3, so the operation prescribed is:
973 |→ 97 + (5 × 3) = 112.
We can repeat the same operation with the number 112. Its last digit is 2, so the operation
prescribed is:
112 |→ 11 + (5 × 2) = 21.
Note that both 21 and 973 are multiples of 7.

 I'm proud of Chika! He took the initiative to do this and his name will forever be used for this method.

The other divisibility rules are:

• 0: do not ever ever divide by zero. It is illegal.
• 1: every number is divisible by 1 and the quotient is the same number.
• 2: all even numbers are divisible by 2
• 3: if the sum of the digits is divisible by 3, then the number is divisible by 3
• 4: If the last 2 digits are divisible by 4, then the number is divisible by 4
• 5: any number ending in 0 or 5 is divisible by 5
• 6: if a number is divisible by 2 AND 3, it is divisible by 6
• 7: see above
• 8: if the last 3 digits are divisible by 8, then the number is divisible by 8
• 9: if the sum of the digits is divisible by 9, then the number is divisible by 9
• 10: any number ending in zero is divisible by 10

So have fun with your math and your puzzles this year! Maybe you can find a divisibility rule for 11, 12, 13, or some other number!

Clue: think multiples and addends. 

_/\_/\_