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Question 1 / 3
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1
Find the highest common factor (HCF) of 18, 108, and 264.
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Solution: Step 1: Factorize each number into its prime factors. Step 2: 18 = 2 * 3^2, 108 = 2^2 * 3^3, 264 = 2^3 * 3 * 11. Step 3: Identify the common prime factors: 2 and 3. Step 4: Determine the lowest power of common prime factors: 2^1 * 3^1 = 2 * 3 = 6. Step 5: The HCF of 18, 108, and 264 is 6.
2
Three equilateral triangles have side lengths of 114 units, 76 units, and 152 units. What is the largest possible scale size that can measure all three sides exactly without leaving a remainder?
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Solution: Step 1: Find the greatest common divisor (GCD) of the side lengths 114, 76, and 152. Step 2: Apply Euclidean algorithm: GCD(114, 76) = GCD(76, 38) = 38. Step 3: Verify GCD(38, 152) = 38. Step 4: The largest scale size that can measure all sides exactly is 38 units.
3
A person arranges 17424 items in a square grid such that the number of rows equals the number of items in each row. How many items are in each row?
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Solution: Step 1: Recognize the problem requires finding the square root of 17424. Step 2: Calculate the square root: √17424 = 132. Step 3: Verify 132 * 132 = 17424, confirming the correct number of items per row.
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