Modular arithmetic calculator

What is modular arithmetic calculator?

This modulo calculator performs arithmetic operations modulo p over a given math expression. While you still can simply enter an integer number to calculate its remainder of Euclidean division by a given modulus, this modulo calculator can do much more.

Why is 1 mod 4 1?

1 mod 4 equals 1, since 1/4 = 0 with a remainder of 1. To find 1 mod 4 using the modulus method, we first find the highest multiple of the divisor, 4 that is equal to or less than the dividend, 1. Then, we subtract the highest multiple from the dividend to get the answer to 1 mod 4. Multiples of 4 are 0, 4, 8, 12, etc.

Why is 4 mod 6 4?

To find 4 mod 6 using the Modulo Method, we first divide the Dividend (4) by the Divisor (6). Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (6). Thus, the answer to "4 mod 6?" is 4.

Why is 1 mod 3 1?

1 mod 3 equals 1, since 1/3 = 0 with a remainder of 1. To find 1 mod 3 using the modulus method, we first find the highest multiple of the divisor, 3 that is equal to or less than the dividend, 1. Then, we subtract the highest multiple from the dividend to get the answer to 1 mod 3. Multiples of 3 are 0, 3, 6, 9, etc.

How to solve 4 mod 2?

Explanation: 4 mod 2 equals 0, since 4/2 = 2, with a remainder of 0. To find 4 mod 2 using the modulus method, we first find the highest possible multiple of the divisor, 2 that is equal to or less than the dividend, 4. Then, we subtract the highest multiple from the dividend to get the answer to 4 mod 2.

Why is 1 mod 5 1?

To find 1 mod 5 using the Modulo Method, we first divide the Dividend (1) by the Divisor (5). Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (5). Thus, the answer to "What is 1 mod 5?" is 1.

What does 1 mod 8 mean?

1 mod 8 is short for 1 modulo 8 and it can also be called 1 modulus 8. Modulo is the operation of finding the Remainder when you divide two numbers. Therefore, when you ask "What is 1 mod 8?" you are asking "What is the Remainder when you divide 1 by 8?".

How to solve 4 mod 5?

Thus, the answer to "What is 4 mod 5?" is 4. To find 4 mod 5 using the Modulus Method, we first find the highest multiple of the Divisor (5) that is equal to or less than the Dividend (4). Thus, once again, the answer to "What is 4 mod 5?" is 4.

What does 5mod2 mean?

For example, the expression "5 mod 2" would evaluate to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0; there is nothing to subtract from 9 after multiplying 3 times 3.

How to solve 2 mod 3?

2 mod 3 equals 2, since 2/3 = 0 with a remainder of 2. To find 2 mod 3 using the modulus method, we first find the highest multiple of the divisor, 3 that is equal to or less than the dividend, 2. Then, we subtract that highest multiple of the divisor from the dividend to get the answer to 2 modulus 3 (2 mod 3):

Why is 2 mod 5 equal to 2?

To find 2 mod 5 using the Modulo Method, we first divide the Dividend (2) by the Divisor (5). Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (5). Thus, the answer to "What is 2 mod 5?" is 2.

What does 1 mod 6 mean?

The "mod 6" means that we are working only with the remainders of numbers after division by 6, and not really working with the integers at all. Note that this word "mod" is different from the modulus operator used in programming languages. Even though "4+3 = 1 mod 6" in English is true, "4+3 == 1%6" in C is false.

What is the answer for 10 mod 3?

First, we divide 10 by 3. We see that the remainder is 1, which is the second step, and this tells us that 10 mod 3 = 1. Not hard at all!

How to calculate mod 26?

Mathematically, we write equivalent as ≡. For example, the elements of the integers modulo (often shortened to “mod”) 26 are 0,1,...,24,25. Then 31 is equivalent to 5 modulo 26, written 31 ≡ 5 mod 26, because when 31 is divided by 26 the remainder is 5. Similarly, we also have 57 ≡ 5 mod 26.

How to calculate mod 26?

Why is 4 mod 10 4?

To find 4 mod 10 using the Modulo Method, we first divide the Dividend (4) by the Divisor (10). Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (10). Thus, the answer to "What is 4 mod 10?" is 4.

How to solve 2 mod 3?

How do you solve a modular arithmetic addition?

Properties of addition in modular arithmetic:

If a + b = c , then a ( mod N ) + b ( mod N ) ≡ c ( mod N ) . If a ≡ b ( mod N ) , then a + k ≡ b + k ( mod N ) for any integer . If a ≡ b ( mod N ) , and c ≡ d ( mod N ) , then a + c ≡ b + d ( mod N ) .

What is the mod of 25 and 7?

To find 25 mod 7 using the Modulo Method, we first divide the Dividend (25) by the Divisor (7). Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (7). Thus, the answer to "What is 25 mod 7?" is 4.

What is the value of 13 in mod4?

Thus, the answer to "What is 13 mod 4?" is 1. To find 13 mod 4 using the Modulus Method, we first find the highest multiple of the Divisor (4) that is equal to or less than the Dividend (13). Thus, once again, the answer to "What is 13 mod 4?" is 1.

What is 15 inverse mod 26?

So, the inverse of 15 modulo 26 is 7 (and the inverse of 7 modulo 26 is 15). Gcd(6, 26) = 2; 6 and 26 are not relatively prime. Therefore, 6 does not have a multiplicative inverse modulo 26.

How to calculate mod 5?

The modulus is another name for the remainder after division. For example, 17 mod 5 = 2, since if we divide 17 by 5, we get 3 with remainder 2.

How to solve 3 mod 10?

First, we divide 10 by 3. We see that the remainder is 1, which is the second step, and this tells us that 10 mod 3 = 1. Not hard at all!

How to solve 8 mod 3?

To find 8 mod 3 using the Modulo Method, we first divide the Dividend (8) by the Divisor (3). Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (3). Thus, the answer to "What is 8 mod 3?" is 2.

How to solve 3 mod 7?

Mod just means you take the remainder after performing the division. When you divide 3 by 7 you get 3= 0*7 + 3 which means that the remainder is 3.

What does 2 mod 4 mean?

mod means the reaminder when divided by. So 2 divided by 4 is 0 with 2 remaining. Therefore 2 mod 4 is 2.

What does 0 mod 4 mean?

Answer and Explanation: 0 mod n = 0 for any n. It is simply because 0 cannot be divided, and since the division is undefined there are no remainders left.