Solve (1+2+6+24+5*4*3*2*4+6*5*3*2*1+7*6*5*4*3*2*1)%6

$$(1+2+6+24+5 \times 4 \times 3 \times 2 \times 4+6 \times 5 \times 3 \times 2 \times 1+7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1) \% 6$$

Evaluate

$$\frac{17199}{50}=343.98$$

Solution Steps

Multiply 5 and 4 to get 20. Multiply 6 and 5 to get 30. Multiply 7 and 6 to get 42.

$$\frac{1+2+6+24+20\times 3\times 2\times 4+30\times 3\times 2\times 1+42\times 5\times 4\times 3\times 2\times 1}{100}\times 6$$

Add 1 and 2 to get 3.

$$\frac{3+6+24+20\times 3\times 2\times 4+30\times 3\times 2\times 1+42\times 5\times 4\times 3\times 2\times 1}{100}\times 6$$

Add 3 and 6 to get 9.

$$\frac{9+24+20\times 3\times 2\times 4+30\times 3\times 2\times 1+42\times 5\times 4\times 3\times 2\times 1}{100}\times 6$$

Add 9 and 24 to get 33.

$$\frac{33+20\times 3\times 2\times 4+30\times 3\times 2\times 1+42\times 5\times 4\times 3\times 2\times 1}{100}\times 6$$

Multiply 20 and 3 to get 60.

$$\frac{33+60\times 2\times 4+30\times 3\times 2\times 1+42\times 5\times 4\times 3\times 2\times 1}{100}\times 6$$

Multiply 60 and 2 to get 120.

$$\frac{33+120\times 4+30\times 3\times 2\times 1+42\times 5\times 4\times 3\times 2\times 1}{100}\times 6$$

Multiply 120 and 4 to get 480.

$$\frac{33+480+30\times 3\times 2\times 1+42\times 5\times 4\times 3\times 2\times 1}{100}\times 6$$

Add 33 and 480 to get 513.

$$\frac{513+30\times 3\times 2\times 1+42\times 5\times 4\times 3\times 2\times 1}{100}\times 6$$

Multiply 30 and 3 to get 90.

$$\frac{513+90\times 2\times 1+42\times 5\times 4\times 3\times 2\times 1}{100}\times 6$$

Multiply 90 and 2 to get 180.

$$\frac{513+180\times 1+42\times 5\times 4\times 3\times 2\times 1}{100}\times 6$$

Multiply 180 and 1 to get 180.

$$\frac{513+180+42\times 5\times 4\times 3\times 2\times 1}{100}\times 6$$

Add 513 and 180 to get 693.

$$\frac{693+42\times 5\times 4\times 3\times 2\times 1}{100}\times 6$$

Multiply 42 and 5 to get 210.

$$\frac{693+210\times 4\times 3\times 2\times 1}{100}\times 6$$

Multiply 210 and 4 to get 840.

$$\frac{693+840\times 3\times 2\times 1}{100}\times 6$$

Multiply 840 and 3 to get 2520.

$$\frac{693+2520\times 2\times 1}{100}\times 6$$

Multiply 2520 and 2 to get 5040.

$$\frac{693+5040\times 1}{100}\times 6$$

Multiply 5040 and 1 to get 5040.

$$\frac{693+5040}{100}\times 6$$

Add 693 and 5040 to get 5733.

$$\frac{5733}{100}\times 6$$

Express \frac{5733}{100}\times 6 as a single fraction.

$$\frac{5733\times 6}{100}$$

Multiply 5733 and 6 to get 34398.

$$\frac{34398}{100}$$

Reduce the fraction \frac{34398}{100} to lowest terms by extracting and canceling out 2.

$$\frac{17199}{50}$$

Factor

$$\frac{3 ^ {3} \cdot 7 ^ {2} \cdot 13}{2 \cdot 5 ^ {2}} = 343\frac{49}{50} = 343.98$$