Answer :
Final answer:
The Highest Common Factor (HCF) of 14, 36, and 175 cannot be found by dividing 14 by the other numbers as they do not divide evenly. However, using the Euclidean algorithm method, the HCF of 14, 36, and 175 is 1.
Explanation:
To find the Highest Common Factor (HCF) of 14, 36, and 175 by the division method, you first look for the smallest number, which is 14. This is the dividend. You then divide 14 by each of the other numbers, one after the other. In this case, because neither 36 nor 175 is divisible by 14 without a remainder, you can't find the HCF using this method.
However, we can find the HCF using the other method which is Euclidean algorithm. Here's how:
- Divide the highest number by the next highest number and find the remainder. (175 / 36 = 4 remainder 23)
- Take the divisor and divide by the remainder from step 1. (36 / 23 = 1 remainder 13)
- Continue this process until the remainder is 0. The last non-zero remainder is the HCF of the number. In this case, it continues like this: 23 / 13 = 1 remainder 10, 13 / 10 = 1 remainder 3, 10 / 3 = 3 remainder 1, 3 / 1 = 3 remainder 0. So, 1 is the HCF of the numbers.
Remember the key in using the division method to find the HCF is to continue this process until the remainder is zero and the last non-zero remainder is your HCF.p>
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