Why does divisibility rule by 3 work

The divisibility rule of eleven states that we must subtract and then add the digits in an alternating pattern from left to right; if the answer is 0 or 11 then the result is divisible by Is 0 an even number?

Zero is an even number. In other words, its parity—the quality of an integer being even or odd—is even. Is 41 a prime number? All numbers that end in five are divisible by five. Therefore all numbers that end with five and are greater than five are composite numbers. The prime numbers between 2 and are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and What is the rule of 3 in math? The Rule of Three is a Mathematical Rule that allows you to solve problems based on proportions.

How do you know a number is divisible by 8? The Rule for 8: If the last three digits of a whole number are divisible by 8, then the entire number is divisible by 8. For this rule, we will look at the last three digits of the number: ,, Does 8 divide evenly into ? You can generalize it to n digit numbers. The idea is to express the n digit numbers in powers of Let abc be a 3 digit number divisible by 3.

Since you tagged it abstract-algebra let's use a little algebra to help clarify the essence of the matter. The key point is that radix representation is a polynomial function of the radix, and polynomials being compositions of sums and products are compatible with modular arithmetic, i.

See also the universal divisibility test. So a number whose sum is 3. Which is divisible by 3. It's clear from this representation. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Asked 8 years, 7 months ago. Active 6 months ago. Viewed 81k times. Bill Dubuque k 36 36 gold badges silver badges bronze badges. Aj Aj 1 1 gold badge 4 4 silver badges 7 7 bronze badges.

And write out the expansion in decimals. Do you know modular arithmetic? Divisibility Rule of 3 The divisibility rule of 3 states that if the sum of the digits of a whole number is a multiple of 3, then the original number is also divisible by 3. What is the Divisibility Rule of 3? Divisibility Rule of 3 for Large Numbers 3.

Divisibility Rule of 3 and 9 4. Divisibility Test of 3 and 4 5. Divisibility Rule of 3 Examples 6. Divisibility Rule of 3 Examples Example 1: For the following numbers, using the test of divisibility by 3, find out whether the numbers are divisible by 3 or not.

Have questions on basic mathematical concepts? Become a problem-solving champ using logic, not rules. Learn the why behind math with our certified experts. Explore math program. Explore coding program. Divisibility Rules Worksheet. Math worksheets and visual curriculum. This means the test can be applied to a number with any number of digits. Click to see it. Thinking about remainders, it's possible to devise a divisibility test for any number.

Click to read more. Thinking about remainders, it's possible to check the answers to calculations involving multiplication. An alternative way to think about using remainders is to use modular arithmetic see the article Modular Arithmetic.

With some ingenuity, particular tests can be contrived for some integers.