Eulclid's Division Lemma
Ask students to guess two numbers, for first instance one large and one small.
Now ask them if they can divide the large one by the small one, not considering the remainder what could be.
Then ask them to express the large number as multiple of small number added a fixed number to it.
E.g. Guessed two numbers are 375, 43
Ask them if 375 can be expressed as multiple of 43?
Yes! 43 X 8 = 344, if 31 is added to it.
Ask them any number can be expressed so?
Yes!
That if there is two numbers, namely FIRST NUMBER and SECOND NUMBER, one of it can be expressed as multiple of the THIRD NUMBER added to it any FOURTH NUMBER.
FIRST NUMBER=SECOND NUMBER X THIRD NUMBER + FOURTH NUMBER
Let some letters refer to each:
a=FIRST NUMBER
b=SECOND NUMBER
q=THIRD NUMBER
r=FOURTH NUMBER
Theory:
If there are two numbers a and b, there exist two unique numbers q and r satisfying:
a=b * q+ r or a= by+r
Ask students to guess two numbers, for first instance one large and one small.
Now ask them if they can divide the large one by the small one, not considering the remainder what could be.
Then ask them to express the large number as multiple of small number added a fixed number to it.
E.g. Guessed two numbers are 375, 43
Ask them if 375 can be expressed as multiple of 43?
Yes! 43 X 8 = 344, if 31 is added to it.
Ask them any number can be expressed so?
Yes!
That if there is two numbers, namely FIRST NUMBER and SECOND NUMBER, one of it can be expressed as multiple of the THIRD NUMBER added to it any FOURTH NUMBER.
FIRST NUMBER=SECOND NUMBER X THIRD NUMBER + FOURTH NUMBER
Let some letters refer to each:
a=FIRST NUMBER
b=SECOND NUMBER
q=THIRD NUMBER
r=FOURTH NUMBER
Theory:
If there are two numbers a and b, there exist two unique numbers q and r satisfying:
a=b * q+ r or a= by+r
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