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29 Oct 2019, 23:45
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Hello, can someone please explain the following question:
Why can the HCF of two numbers, even and odd, never be even?
Thank you!
Why can the HCF of two numbers, even and odd, never be even?
Thank you!
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Hcf is the lowest common power of all the Prime factors of the numbers.
An odd number can never have a even prime factor eg. 9=3^2, 21=7*3 etc
An even number can have both even and odd prime factors eg 6=3*2
So hcf of a even and odd number like 6 and 21 will be 3 (an odd number)
This will always be true because as explained above an odd number can never have an even prime factor
Posted from my mobile device
An odd number can never have a even prime factor eg. 9=3^2, 21=7*3 etc
An even number can have both even and odd prime factors eg 6=3*2
So hcf of a even and odd number like 6 and 21 will be 3 (an odd number)
This will always be true because as explained above an odd number can never have an even prime factor
Posted from my mobile device
07 Nov 2019, 12:21
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Luca1111111111111
The HCF (or GCF) has to be a factor of both numbers. (That's just because of the way that HCF is defined: it's the largest number that's a factor of both.)
However, an odd number does not have any even factors. For example, the factors of 15 are 1, 3, 5, and 15, all odd. Why? Because an even number will never divide evenly into an odd number.
Since the odd number doesn't have any even factors, there can't be any even numbers that are factors of both. So, the HCF can't be an even number.
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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Thank you for understanding, and happy exploring!
