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Algebra Difficulty 1.8 Junior Find the answer

If 2×2×3×3×5×6=5×6×n×n2 \times 2 \times 3 \times 3 \times 5 \times 6=5 \times 6 \times n \times n, what is a possible value of nn?

A number or a short expression. Spacing and $ signs are ignored.

Solution

We rewrite the left side of the given equation as 5×6×(2×3)×(2×3)5 \times 6 \times(2 \times 3) \times(2 \times 3). Since 5×6×(2×3)×(2×3)=5×6×n×n5 \times 6 \times(2 \times 3) \times(2 \times 3)=5 \times 6 \times n \times n, then a possible value of nn is 2×32 \times 3 or 6.

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