Solve 18*17*16*15*14*13*12*11*10*9*8*7div6div5div4div3div2div6div5div4div3div2

$$18 \times 17 \times 16 \times 15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \div 6 \div 5 \div 4 \div 3 \div 2 \div 6 \div 5 \div 4 \div 3 \div 2$$

Evaluate

$$17153136$$

Solution Steps

Express \frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7}{6}}{5}}{4}}{3}}{2}}{6}}{5}}{4}}{3}}{2} as a single fraction.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7}{6}}{5}}{4}}{3}}{2}}{6}}{5}}{4}}{3\times 2}$$

Express \frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7}{6}}{5}}{4}}{3}}{2}}{6}}{5}}{4} as a single fraction.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7}{6}}{5}}{4}}{3}}{2}}{6}}{5\times 4}}{3\times 2}$$

Express \frac{\frac{\frac{\frac{\frac{\frac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7}{6}}{5}}{4}}{3}}{2}}{6} as a single fraction.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7}{6}}{5}}{4}}{3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Express \frac{\frac{\frac{\frac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7}{6}}{5}}{4}}{3} as a single fraction.

$$\frac{\frac{\frac{\frac{\frac{\frac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7}{6}}{5}}{4\times 3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Express \frac{\frac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7}{6}}{5} as a single fraction.

$$\frac{\frac{\frac{\frac{\frac{18\times 17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7}{6\times 5}}{4\times 3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Cancel out 5\times 6 in both numerator and denominator.

$$\frac{\frac{\frac{\frac{3\times 3\times 7\times 8\times 9\times 10\times 11\times 12\times 13\times 14\times 16\times 17}{4\times 3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{\frac{\frac{9\times 7\times 8\times 9\times 10\times 11\times 12\times 13\times 14\times 16\times 17}{4\times 3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Multiply 9 and 7 to get 63.

$$\frac{\frac{\frac{\frac{63\times 8\times 9\times 10\times 11\times 12\times 13\times 14\times 16\times 17}{4\times 3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Multiply 63 and 8 to get 504.

$$\frac{\frac{\frac{\frac{504\times 9\times 10\times 11\times 12\times 13\times 14\times 16\times 17}{4\times 3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Multiply 504 and 9 to get 4536.

$$\frac{\frac{\frac{\frac{4536\times 10\times 11\times 12\times 13\times 14\times 16\times 17}{4\times 3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Multiply 4536 and 10 to get 45360.

$$\frac{\frac{\frac{\frac{45360\times 11\times 12\times 13\times 14\times 16\times 17}{4\times 3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Multiply 45360 and 11 to get 498960.

$$\frac{\frac{\frac{\frac{498960\times 12\times 13\times 14\times 16\times 17}{4\times 3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Multiply 498960 and 12 to get 5987520.

$$\frac{\frac{\frac{\frac{5987520\times 13\times 14\times 16\times 17}{4\times 3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Multiply 5987520 and 13 to get 77837760.

$$\frac{\frac{\frac{\frac{77837760\times 14\times 16\times 17}{4\times 3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Multiply 77837760 and 14 to get 1089728640.

$$\frac{\frac{\frac{\frac{1089728640\times 16\times 17}{4\times 3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Multiply 1089728640 and 16 to get 17435658240.

$$\frac{\frac{\frac{\frac{17435658240\times 17}{4\times 3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Multiply 17435658240 and 17 to get 296406190080.

$$\frac{\frac{\frac{\frac{296406190080}{4\times 3}}{2\times 6}}{5\times 4}}{3\times 2}$$

Multiply 4 and 3 to get 12.

$$\frac{\frac{\frac{\frac{296406190080}{12}}{2\times 6}}{5\times 4}}{3\times 2}$$

Divide 296406190080 by 12 to get 24700515840.

$$\frac{\frac{\frac{24700515840}{2\times 6}}{5\times 4}}{3\times 2}$$

Multiply 2 and 6 to get 12.

$$\frac{\frac{\frac{24700515840}{12}}{5\times 4}}{3\times 2}$$

Divide 24700515840 by 12 to get 2058376320.

$$\frac{\frac{2058376320}{5\times 4}}{3\times 2}$$

Multiply 5 and 4 to get 20.

$$\frac{\frac{2058376320}{20}}{3\times 2}$$

Divide 2058376320 by 20 to get 102918816.

$$\frac{102918816}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{102918816}{6}$$

Divide 102918816 by 6 to get 17153136.

$$17153136$$

Factor

$$2^{4}\times 3^{2}\times 7^{2}\times 11\times 13\times 17$$