Question

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Explanation:

Step1: Understand grid rules

Each row has 2 numbers (from 1-8, no repeats) that multiply to the shaded right number. Each column's 2 numbers multiply to the shaded bottom number.

Step2: Analyze Column 1 (product=30)

Factor pairs of 30 (1-8): $5 \times 6 = 30$. So Column 1 numbers: 5,6.

Step3: Analyze Column 2 (product=6)

Factor pairs of 6 (1-8): $1 \times 6 = 6$ or $2 \times 3 = 6$. Since 6 is used in Column1, use $2 \times 3 = 6$. Column2 numbers: 2,3.

Step4: Analyze Column 3 (product=56)

Factor pairs of 56 (1-8): $7 \times 8 = 56$. Column3 numbers:7,8.

Step5: Analyze Column 4 (product=4)

Factor pairs of 4 (1-8): $1 \times 4 = 4$ or $2 \times 2 = 4$. No repeats, so $1 \times 4 = 4$. Column4 numbers:1,4.

Step6: Solve Row2 (product=2)

Only pair (1-8) is $1 \times 2 = 2$. Assign 1 to Column4, 2 to Column2.
Row2: $\boldsymbol{6, 2, 7, 1, 2}$ (6 from Column1, 2 Column2,7 Column3,1 Column4)

Step7: Solve Row1 (product=15)

Factor pair (1-8): $3 \times 5 = 15$. Assign 3 to Column2,5 to Column1. Remaining Column3=8, Column4=4.
Row1: $\boldsymbol{5, 3, 8, 4, 15}$

Step8: Solve Row3 (product=48)

Available numbers:6(Col1),3(Col2) invalid. Use 6(Col1),8(Col3): $6 \times 8 = 48$. Assign 6 to Column1,8 to Column3, remaining Column2=3, Column4=4 invalid. Correct: $6 \times 8 = 48$, Row3: $\boldsymbol{6, 3, 8, 1, 48}$ (1 from Column4)

Step9: Solve Row4 (product=28)

Factor pair (1-8): $4 \times 7 = 28$. Assign 4 to Column4,7 to Column3, remaining Column1=5, Column2=2.
Row4: $\boldsymbol{5, 2, 7, 4, 28}$

Answer:

Completed grid (rows left to right):

1. 5, 3, 8, 4, 15
2. 6, 2, 7, 1, 2
3. 6, 3, 8, 1, 48
4. 5, 2, 7, 4, 28