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Mar 26, 2013 · Let us have a 3 digit number that can be divided by 3, ie xyz. Therefore xyz=0 (mod3) iff xyz=(100x)+(10y)+z=x+y+z=0(mod3) Therefore x+y+z=0(mod 3), meaning that the sum of the digits is divisible by 3. This is an if and only if statement. You can generalize it to n digit numbers. The idea is to express the n digit numbers in powers of 10.
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According to the divisibility rule of 3, any big number is exactly divisible by 3 if the sum of the digits is a multiple of 3. For example, the number 2,146,497 is exactly divisible by 3, where quotient = 715,499 and remainder = 0. The sum of all digits is 2 + 1 + 4 + 6 + 4 + 9 + 7 = 33 and 33 is exactly divisible by 3.
If you can divide a number A by a number B, without remainder, we say that B is a factor (or divisor) of A, and that A is a multiple of B. We often write B|A, where the vertical bar simply means “divides”. For example, 7 × 3 = 21, so 7 is a factor multiple of 21. Similarly, 21 is a multiple factor of 7, and we can write 7|21.
The result of multiplying real numbers is called the product and the result of dividing is called the quotient. Recall that multiplication is equivalent to adding: 3 ⋅ 4 = 4 + 4 + 4 = 12. Clearly, the product of two positive numbers is positive. Similarly, the product of a positive number and negative number can be written as shown: We see ...
For example a number (which I randomly grab from the top of my head): 289752. whose digits sum to 33 (2+8+9+7+5+2=33) That sum 33 is divisible by three and so is the original number 289752. This is not the case when dividing by 2, for example 12 is divisible by two but when its digits are summed (1+2=3) you receive 3 which is NOT divisible by 2.
Math Calculator. Step 1: Enter the expression you want to evaluate. The Math Calculator will evaluate your problem down to a final solution. You can also add, subtraction, multiply, and divide and complete any arithmetic you need. Step 2: Click the blue arrow to submit and see your result! Math Calculator from Mathway will evaluate various math ...
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The divisibility rule of 9 9 tells us that 1 + 2 + a + b 1+2+ a+b is a multiple of 9. 9. Since it is a number from 3 3 to 21, 21, it must be either 9 9 or 18. 18. Now, the divisibility rule of 11 11 tells us that 1 - 2 + a - b 1 −2+a− b is a multiple of 11. 11. Since it is a number from -10 −10 to 8, 8, it must be 0.
