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What is the Highest Common Factor of 403, 434 and 465?

Understanding HCF

The highest common factor, or HCF, is the largest number that two or more numbers have in common. In other words, it is the highest number that divides exactly into all of the numbers in question. For example, the HCF of 12, 24 and 36 is 12, because 12 is the highest number that divides exactly into all three numbers.

Calculating the HCF of 403, 434 and 465

In order to calculate the HCF of 403, 434 and 465, we need to find the prime factors of each of the numbers. To do this, we can write each number as a product of its prime factors. For example, 403 can be written as 7 x 3 x 3 x 3, 434 can be written as 2 x 7 x 31, and 465 can be written as 5 x 7 x 11.

Once we have the prime factors of each number, we can look for any prime factors that are common to all three numbers. In this case, the common prime factors are 7 and 3. We then multiply these common prime factors together to get the HCF. In this case, the HCF of 403, 434 and 465 is 7 x 3, which is 21.

Conclusion

In conclusion, the HCF of 403, 434 and 465 is 21. This is the highest number that divides exactly into all three numbers. To calculate the HCF, we need to find the prime factors of each number, and then multiply any common prime factors together.

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