Solve 1*2*3+2*3*4+3*4*5+4*5*6+5*6*7+6*7*8+7*8*9+8*9*10+9*10*11+10*11*12+11*12*13+12*13*14+13*14*15

$$1 \times 2 \times 3+2 \times 3 \times 4+3 \times 4 \times 5+4 \times 5 \times 6+5 \times 6 \times 7+6 \times 7 \times 8+7 \times 8 \times 9+8 \times 9 \times 10+9 \times 10 \times 11+10 \times 11 \times 12+11 \times 12 \times 13+12 \times 13 \times 14+13 \times 14 \times 15$$

Evaluate

$$10920$$

Solution Steps

Multiply 1 and 2 to get 2. Multiply 2 and 3 to get 6. Multiply 3 and 4 to get 12. Multiply 4 and 5 to get 20. Multiply 5 and 6 to get 30. Multiply 6 and 7 to get 42. Multiply 7 and 8 to get 56. Multiply 8 and 9 to get 72. Multiply 9 and 10 to get 90. Multiply 10 and 11 to get 110. Multiply 11 and 12 to get 132. Multiply 12 and 13 to get 156. Multiply 13 and 14 to get 182.

$$2\times 3+6\times 4+12\times 5+20\times 6+30\times 7+42\times 8+56\times 9+72\times 10+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Multiply 2 and 3 to get 6.

$$6+6\times 4+12\times 5+20\times 6+30\times 7+42\times 8+56\times 9+72\times 10+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Multiply 6 and 4 to get 24.

$$6+24+12\times 5+20\times 6+30\times 7+42\times 8+56\times 9+72\times 10+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Add 6 and 24 to get 30.

$$30+12\times 5+20\times 6+30\times 7+42\times 8+56\times 9+72\times 10+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Multiply 12 and 5 to get 60.

$$30+60+20\times 6+30\times 7+42\times 8+56\times 9+72\times 10+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Add 30 and 60 to get 90.

$$90+20\times 6+30\times 7+42\times 8+56\times 9+72\times 10+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Multiply 20 and 6 to get 120.

$$90+120+30\times 7+42\times 8+56\times 9+72\times 10+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Add 90 and 120 to get 210.

$$210+30\times 7+42\times 8+56\times 9+72\times 10+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Multiply 30 and 7 to get 210.

$$210+210+42\times 8+56\times 9+72\times 10+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Add 210 and 210 to get 420.

$$420+42\times 8+56\times 9+72\times 10+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Multiply 42 and 8 to get 336.

$$420+336+56\times 9+72\times 10+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Add 420 and 336 to get 756.

$$756+56\times 9+72\times 10+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Multiply 56 and 9 to get 504.

$$756+504+72\times 10+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Add 756 and 504 to get 1260.

$$1260+72\times 10+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Multiply 72 and 10 to get 720.

$$1260+720+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Add 1260 and 720 to get 1980.

$$1980+90\times 11+110\times 12+132\times 13+156\times 14+182\times 15$$

Multiply 90 and 11 to get 990.

$$1980+990+110\times 12+132\times 13+156\times 14+182\times 15$$

Add 1980 and 990 to get 2970.

$$2970+110\times 12+132\times 13+156\times 14+182\times 15$$

Multiply 110 and 12 to get 1320.

$$2970+1320+132\times 13+156\times 14+182\times 15$$

Add 2970 and 1320 to get 4290.

$$4290+132\times 13+156\times 14+182\times 15$$

Multiply 132 and 13 to get 1716.

$$4290+1716+156\times 14+182\times 15$$

Add 4290 and 1716 to get 6006.

$$6006+156\times 14+182\times 15$$

Multiply 156 and 14 to get 2184.

$$6006+2184+182\times 15$$

Add 6006 and 2184 to get 8190.

$$8190+182\times 15$$

Multiply 182 and 15 to get 2730.

$$8190+2730$$

Add 8190 and 2730 to get 10920.

$$10920$$

Factor

$$2^{3}\times 3\times 5\times 7\times 13$$