what is mod 10 So for example 24 modulo 10 and 34 modulo 10 give the same answer 4 Therefore 24 and 34 are congruent modulo 10 Let s have a look at another example 9 21 mod 6 because 21 9 12 is a multiple of 6 It can also be written in short as 6 21 9 Or equivalently 21 and 9 have the same remainder when we divide them by 6 9
Example 1 mod 2 1 mod 2 is a situation where the divisor 2 is larger than the dividend 1 so the remainder you get is equal to the dividend 1 For 1 divided by 2 2 goes into 1 zero times with a remainder of 1 So 1 mod 2 1 Similarly 5 mod 10 5 since 10 divides into 5 zero times with 5 left over as the remainder Modulo This article is about the binary operation mod a n For the mod n notation see Modular arithmetic For other uses see Modulo disambiguation In computing the modulo operation returns the remainder or signed remainder of a division after one number is divided by another called the modulus of the operation
what is mod 10
what is mod 10
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The modulo or modulus or mod is the remainder after dividing one number by another Example 100 mod 9 equals 1 Because 100 9 11 with a remainder of 1 Another example 14 mod 12 equals 2 Because 14 12 1 with a remainder of 2 12 hour time uses modulo 12 14 o clock becomes 2 o clock It is where we end up not how many times around Examples 8 mod 4 With a modulus of 4 we make a clock with numbers 0 1 2 3 We start at 0 and go through 8 numbers in a clockwise sequence 1 2 3 0 1 2 3 0 We ended up at 0 so 8 mod 4 0 7 mod 2 With a modulus of
The modulo or modulus or mod is the remainder after dividing one number by another Example 100 mod 9 equals 1 Because 100 9 11 with a remainder of 1 12 Hour Time 12 hour time uses modulo 12 Example 14 mod 12 equals 2 Because 14 12 1 with a remainder of 2 So 14 o clock becomes 2 o clock For instance if we add the sum of 2 4 3 and 7 the sum is congruent to 6 mod 10 That s 16 mod 10 This means 16 divided by 10 leaves a remainder of 6
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Definition Modulo Let m in mathbb Z a is congruent to b modulo m denoted as a equiv b mod n if a and b have the remainder when they are divided by n for a b in mathbb Z Example Then a mod n r Alternatively we can say that a mod n r if and only if n divides a r without remainder For instance 21 mod 5 1 because 21 4 5 1 23 mod 10 3 because 23 2 10 3 3 mod 10 3 because 3 0 10 3
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