Browsing category factorising

Factorising a large number, part II: Gaussian integers

You know how things escalate on Twitter sometimes? Somebody makes an off-hand comment wondering whether a number is prime and suddenly you're neck deep in number theory? This is the story of how you might factorise 842,909 on paper. In fact, it's the second part of the story; we join

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Factorising a large number, part I: Sums of squares in different ways

There is a theorem that states: if a number can be written as the sum of two squares in two different ways, it is composite. Because of Twitter, I became interested in factorising $n=842,909$. Can this be written as the sum of two squares1? How - without cheating and using

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Ask Uncle Colin: Factors!

Dear Uncle Colin, If you know all of the factors of $n$, can you use that to find all of the factors of $n^2$? For example, I know that 6 has factors 1, 2, 3 and 6. Its square, 36, has the same factors, as well as 4, 9, 12,

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Factorise or factor?

@onthisdayinmath asks: Is it just me or has "factorise" (with s or z) suddenly become much more common term for "to factor" recently? Before I went to America, I had never seen factor used as a verb, at least in a mathematical context: you don't ration a denominator, so why

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Simplifying algebraic fractions (GCSE algebra)

Towards the end of a GCSE paper, you're quite frequently asked to simplify an algebraic fraction like: $\frac{4x^2 + 12x - 7}{2x^2 + 5x - 3}$ Hold back the tears, dear students, hold back the tears. These are easier than they look. There's one thing you need to know: algebraic

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Simplifying algebraic fractions (GCSE algebra)

Towards the end of a GCSE paper, you're quite frequently asked to simplify an algebraic fraction like: $\frac{4x^2 + 12x - 7}{2x^2 + 5x - 3}$ Hold back the tears, dear students, hold back the tears. These are easier than they look. There's one thing you need to know: algebraic

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Figuring out roots of horrible numbers

"$1296$?!" said the student. "They want me to find the fourth root of $1296$?" "Evidently," I said. The air turned, for a moment, blue. "Well, how about factorising it?" A different shade of blue. A whirring of pencil. A mutter of 648, a grumble of 324, a harrumph of 162,

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GCSE Factorising revision

A quick, one-off masterclass in how to put things into brackets today - six methods of factorising you need to know to do well at GCSE maths. (1) Common number $3a + 6$ two terms (letter and number, no squares) you can divide them both by 3 $3 \times a

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