What is 3 Mod 78? (3 % 78)
In this article we're going to look at what 3 mod 78 means and how we can calculate that. This type of divisibility operation is called mod, modulo or modulus and you can often see the symbol % used as well (i.e. 3 % 78)
Modulo is the mathematical operation which lets you find the remainder when dividing two numbers like 3 and 78 together. When are say "what is 3 % 78?" we are asking "when I divide 3 by 78, what is the remainder?"
In math, we use modulo frequently. It can be used to check if a number is even or odd, clocks use it to tell the time, and you can use it to count something for a certain number of times as well.
Before we begin, let's cover the terms you need to know:
- The first number, 3, is called the dividend
- The second number, 78, is called the divisor
- When you divide 3 by 78, the answer is called the quotient
- The quotient is made up of the whole number part (called the whole) and the decimal places part (called the fractional)
To calculate 3 mod 78 we first need to divide 3 by 78 to get the quotient:
Now we have the quotient, we take the whole part of it (0) and multiply it by the divisor (78):
We then take the result of that calculation and subtract it from the dividend to get the answer:
3 - 0 = 3
Therefore, the final answer is:
3 mod 78 = 3
We could also calculate this using a different method. To use this method, list out all of the multiples of the divisor (78) and find the one that is equal to or less than the dividend (3).
The multiples of 78 are: 0, 78, 156, 234, and so on.
As we look at those multiples of 78 we can see that the highest number that is less than or equal to the dividend (3) is 0.
Once we have that number, we subtract 0 from the dividend to get our answer:
3 - 0 = 3
Therefore, the solution using this method is the same as the previous modulo method:
3 mod 78 = 3
If you enjoyed this article I challenge you now to calculate some problems yourself or use the list below to read up on how to calculate this with different numbers and try to work out it out for yourself.
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