Find HCF of 360, 504 and 864 using continued division.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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To find the Highest Common Factor (HCF) of 360, 504, and 864 using continued division, we'll first find the HCF of two numbers, and then find the HCF of that result and the third number.
Step 1: Find the HCF of 360 and 504.
Divide 504 by 360:
504 = 1 × 360 + 144
Divide 360 by the remainder 144:
360 = 2 × 144 + 72
Divide 144 by the remainder 72:
144 = 2 × 72 + 0
The HCF of 360 and 504 is 72.
Step 2: Find the HCF of the result from Step 1 (72) and the third number (864).
Divide 864 by 72:
864 = 12 × 72 + 0
The HCF of 72 and 864 is 72.
Therefore, the HCF of 360, 504, and 864 is 72.
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