Factoring is traditionally considered an “f-word” for students of math. But it sometimes has its good sides (which I’ll show over the next couple of days).

In the meantime, I’ll show the two ways (that I know) to factor numbers.

This method’s called a factor tree:

You don’t have to put the primes in order for it to be “right.” But it helps for later things.

Here’s another tree:

Here’s another way to factor using an upside division bar-type thing:

Remember, we don’t factor for the sake of factoring. This is only a tool to use when we do other stuff. You’ll see some of this in tomorrow’s post. Here’s one last example:

The way you factor is personal preference. Pick the one you like, or flip-flop. There’re no rules!

Share your preference (or a different way) in the comments!

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I prefer the upside down division way, because you can use it to factor more than one number at once, giving you the GCF and the LCM…the GCF is whatever you can pull out of both, (the stuff on the left side) and the LCM is the GCF multiplied by whatever is leftover at the bottom (the stuff at the left multiplied by the stuff at the bottom–it makes an L shape too).

You can also use it to simplify fractions. Your simplified fraction is whatever is leftover at the bottom.

I’ve never seen it done with more than one number at once. Do you have a sample? That sounds cool.

Maybe this:

EUCLID’S DIVISION LEMNA

Euclid’s division lemma, states that for any two positive integers ‘a’ and ‘b’ we can find two whole numbers ‘q’ and ‘r’ such that

Euclid’s division lemma can be used to:

Find the highest common factor of any two positive integers and to show the common properties of numbers.

Finding H.C.F using Euclid’s division lemma:

Suppose, we have two positive integers ‘a’ and ‘b’ such that ‘a’ is greater than ‘b’. Apply Euclid’s division lemma to the given integers ‘a’ and ‘b’ to find two whole numbers ‘q’ and ‘r’ such that, ‘a’ is equal to ‘b’ multiplied by ‘q’ plus ‘r’.

Check the value of ‘r’. If ‘r’ is equal to zero then ‘b’ is the HCF of the given numbers. If ‘r’ is not equal to zero, apply Euclid’s division lemma to the new divisor ‘b’ and remainder ‘r’. Continue this process till the remainder ‘r’ becomes zero. The value of the divisor ‘b’ in that case is the HCF of the two given numbers.

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Another cool equality is that the product of any 2 numbers is equal to the product of their HCF by their SCM

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I al;so tell my students that you don’t REALLY need the SCM to add fraction. You can do it using the product of the denominators as the common denominator. The result just will not always be the simplest fraction.

I too got a cool trick of “5”

multiply by 5 means add a zero at end and half it

Ex- 42×5= 420/2=210

if can’t half it, just get the previous no. to half and add 5 at end

ex- 93×5= 930/2=920/2 5= 465

Vinayak – nice one!

You can also do this with multiplying by 5: Add two zeros and divide by 4. (Or do your trick twice!)