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| Youtube: HCF or GCD |
Q. What is the difference between the HCF and the GCD of two numbers? Is there any difference at all?
A. They are the same. Whereas Highest Common Factor (HCF) is a little bit old-fashioned, but still in use today.
I studied in the UK, and my Discrete Maths teacher (who was 70 years old) used to say that when he was a student, all profs use HCF than GCD and he pointed out that GCD is an American term (he stressed on the rrr in divider).
As I have been taking more lectures in maths, I realised that applied maths lecturers use HCF more than pure maths lecturers.
There is a tendency in which the terminologies of maths standardise, and now I barely heard the term HCF. For myself, I use GCD more than HCF but I still tell people that my old professors prefer the latter.
I simply miss the time when we had diversity of terms.
(Quora.com)
HCF は，GCD と同じ意味だが少し古い言い方であるとか，純粋数学よりも応用数学によく使われるとかの違いが述べられています．
2つ以上の数や式の共通な因数になる数や式を common divisor または common factor と言うわけですが，実際日本語では，数の場合には公約数，式の場合には共通因数と言うことが多いようです．式の因数分解のときに｢共通因数を括り出す｣といいますが，｢公約数を括りだす｣とは言いませんね．以下はあるサイトの因数分解の説明です．
To factorise an algebraic expression, take out the highest common factor and place it in front of the brackets. Then the expression inside the brackets is obtained by dividing each term by the highest common factor.
(mathteacher.com)例えば，$3a^4b+12a^2b^3=3a^2b(a^2+4b^2)$ と因数分解できますが，このときの HCF は $3a^2b$ ということになります．
因みに，HCF を直訳すれば｢最高共通因数｣となりますが，この訳語はあまり見られず，かろうじて｢プリンストン数学大全｣（朝倉書店 2015年）で使われているのを見つけることができました．
[HCF 問題]
Find the HCF of 240 and 924.
（正解はこちら）
[Reference]
What is the difference between the HCF and the GCD of two numbers? Is there any difference at all?
https://www.quora.com/What-is-the-difference-between-the-HCF-and-the-GCD-of-two-numbers-Is-there-any-difference-at-all
Factorisation using the Common Factor
