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Modulo, remainder calculator. Mod meaning

 Dividend Division , 10 mod 3 = 1
What is modulo? What does it mean? How to determine it? Modulo is a term of arithmetic. It can be expressed using formula
a = b mod n. a is a remainder (modulo), when b is divided by n. In other words b is equal to a, which is multiplied by some integer k plus remainder a: b = k * n + a. Modulo is integer division problem, when we want to split something and get integer values. These two formulas explain clearly, what is remainder. Sometimes mod is changed to percent sign (%).

For example: we have 10 apples in a bag. We want to give it to people equally. We need to split them into three equal parts. We don't want to cut the apples. Formula is 10/3. But it will be with some fraction. Every person will get 3 apples. But one apple will remain in the bag. This one apple is a modulo (remainder).

Another example: we hired five miners. They found eleven gems and wanted to divide equally for everyone. Every miner will get two gems. One gem will remain, because no one will want to break it into pieces. As we all know it can become worthless. This one gem is a modulo.

Remainders, when divider is 3

 1 mod 3 = 1 26 mod 3 = 2 51 mod 3 = 0 76 mod 3 = 1 2 mod 3 = 2 27 mod 3 = 0 52 mod 3 = 1 77 mod 3 = 2 3 mod 3 = 0 28 mod 3 = 1 53 mod 3 = 2 78 mod 3 = 0 4 mod 3 = 1 29 mod 3 = 2 54 mod 3 = 0 79 mod 3 = 1 5 mod 3 = 2 30 mod 3 = 0 55 mod 3 = 1 80 mod 3 = 2 6 mod 3 = 0 31 mod 3 = 1 56 mod 3 = 2 81 mod 3 = 0 7 mod 3 = 1 32 mod 3 = 2 57 mod 3 = 0 82 mod 3 = 1 8 mod 3 = 2 33 mod 3 = 0 58 mod 3 = 1 83 mod 3 = 2 9 mod 3 = 0 34 mod 3 = 1 59 mod 3 = 2 84 mod 3 = 0 10 mod 3 = 1 35 mod 3 = 2 60 mod 3 = 0 85 mod 3 = 1 11 mod 3 = 2 36 mod 3 = 0 61 mod 3 = 1 86 mod 3 = 2 12 mod 3 = 0 37 mod 3 = 1 62 mod 3 = 2 87 mod 3 = 0 13 mod 3 = 1 38 mod 3 = 2 63 mod 3 = 0 88 mod 3 = 1 14 mod 3 = 2 39 mod 3 = 0 64 mod 3 = 1 89 mod 3 = 2 15 mod 3 = 0 40 mod 3 = 1 65 mod 3 = 2 90 mod 3 = 0 16 mod 3 = 1 41 mod 3 = 2 66 mod 3 = 0 91 mod 3 = 1 17 mod 3 = 2 42 mod 3 = 0 67 mod 3 = 1 92 mod 3 = 2 18 mod 3 = 0 43 mod 3 = 1 68 mod 3 = 2 93 mod 3 = 0 19 mod 3 = 1 44 mod 3 = 2 69 mod 3 = 0 94 mod 3 = 1 20 mod 3 = 2 45 mod 3 = 0 70 mod 3 = 1 95 mod 3 = 2 21 mod 3 = 0 46 mod 3 = 1 71 mod 3 = 2 96 mod 3 = 0 22 mod 3 = 1 47 mod 3 = 2 72 mod 3 = 0 97 mod 3 = 1 23 mod 3 = 2 48 mod 3 = 0 73 mod 3 = 1 98 mod 3 = 2 24 mod 3 = 0 49 mod 3 = 1 74 mod 3 = 2 99 mod 3 = 0 25 mod 3 = 1 50 mod 3 = 2 75 mod 3 = 0 100 mod 3 = 1

Remainders of number 10

 10 mod  1 = 0 10 mod  26 = 10 10 mod  51 = 10 10 mod  76 = 10 10 mod  2 = 0 10 mod  27 = 10 10 mod  52 = 10 10 mod  77 = 10 10 mod  3 = 1 10 mod  28 = 10 10 mod  53 = 10 10 mod  78 = 10 10 mod  4 = 2 10 mod  29 = 10 10 mod  54 = 10 10 mod  79 = 10 10 mod  5 = 0 10 mod  30 = 10 10 mod  55 = 10 10 mod  80 = 10 10 mod  6 = 4 10 mod  31 = 10 10 mod  56 = 10 10 mod  81 = 10 10 mod  7 = 3 10 mod  32 = 10 10 mod  57 = 10 10 mod  82 = 10 10 mod  8 = 2 10 mod  33 = 10 10 mod  58 = 10 10 mod  83 = 10 10 mod  9 = 1 10 mod  34 = 10 10 mod  59 = 10 10 mod  84 = 10 10 mod  10 = 0 10 mod  35 = 10 10 mod  60 = 10 10 mod  85 = 10 10 mod  11 = 10 10 mod  36 = 10 10 mod  61 = 10 10 mod  86 = 10 10 mod  12 = 10 10 mod  37 = 10 10 mod  62 = 10 10 mod  87 = 10 10 mod  13 = 10 10 mod  38 = 10 10 mod  63 = 10 10 mod  88 = 10 10 mod  14 = 10 10 mod  39 = 10 10 mod  64 = 10 10 mod  89 = 10 10 mod  15 = 10 10 mod  40 = 10 10 mod  65 = 10 10 mod  90 = 10 10 mod  16 = 10 10 mod  41 = 10 10 mod  66 = 10 10 mod  91 = 10 10 mod  17 = 10 10 mod  42 = 10 10 mod  67 = 10 10 mod  92 = 10 10 mod  18 = 10 10 mod  43 = 10 10 mod  68 = 10 10 mod  93 = 10 10 mod  19 = 10 10 mod  44 = 10 10 mod  69 = 10 10 mod  94 = 10 10 mod  20 = 10 10 mod  45 = 10 10 mod  70 = 10 10 mod  95 = 10 10 mod  21 = 10 10 mod  46 = 10 10 mod  71 = 10 10 mod  96 = 10 10 mod  22 = 10 10 mod  47 = 10 10 mod  72 = 10 10 mod  97 = 10 10 mod  23 = 10 10 mod  48 = 10 10 mod  73 = 10 10 mod  98 = 10 10 mod  24 = 10 10 mod  49 = 10 10 mod  74 = 10 10 mod  99 = 10 10 mod  25 = 10 10 mod  50 = 10 10 mod  75 = 10 10 mod  100 = 10