# Modulo Operation/Examples

## Examples of Use of Modulo Operation

### Modulo Operation: $5 \bmod 3$

$5 \bmod 3 = 2$

### Modulo Operation: $18 \bmod 3$

$18 \bmod 3 = 0$

### Modulo Operation: $-2 \bmod 3$

$-2 \bmod 3 = 1$

### Modulo Operation: $100 \bmod 3$

$100 \bmod 3 = 1$

### Modulo Operation: $100 \bmod 7$

$100 \bmod 7 = 2$

### Modulo Operation: $-100 \bmod 7$

$-100 \bmod 7 = 5$

### Modulo Operation: $-100 \bmod 0$

$-100 \bmod 0 = -100$

### Modulo Operation: $5 \bmod -3$

$5 \bmod -3 = -1$

### Modulo Operation: $18 \bmod -3$

$18 \bmod -3 = 0$

### Modulo Operation: $-2 \bmod -3$

$-2 \bmod -3 = -2$

### Modulo Operation: $1 \cdotp 1 \bmod 1$

$1 \cdotp 1 \bmod 1 = 0 \cdotp 1$

### Modulo Operation: $0 \cdotp 11 \bmod 0 \cdotp 1$

$0 \cdotp 11 \bmod 0 \cdotp 1 = 0 \cdotp 01$

### Modulo Operation: $0 \cdotp 11 \bmod -0 \cdotp 1$

$0 \cdotp 11 \bmod -0 \cdotp 1 = -0 \cdotp 09$

### Modulo Operation: $x \bmod 3 = 2$ and $x \bmod 5 = 3$

Let $x \bmod 3 = 2$ and $x \bmod 5 = 3$.

Then:

$x \bmod 15 = 8$