Using Euclid's algortihm, find the HCF of: 960 and 1575 - Vidyadip

Question

Using Euclid's algortihm, find the $HCF$ of:
$960$ and $1575$

✓

Answer

Dividing $1575$ by $960,$ we get
Quotient $= 1,$ Remainder $= 615$
$\therefore 1575 = 960 × 1 + 615$
Dividing $960$ by $615,$ we get
Quotient $= 1,$ Remainder $= 345$
$\therefore 960 = 615 × 1 + 345$
Dividing $615$ by $345$
Quotient $= 1,$ Remainder $= 270$
$\therefore 615 = 345 × 1 + 270$
Dividing $345$ by $270,$ we get
Quotient $= 1,$ Remainder $= 75$
$\therefore 345 = 270 × 1 + 75$
Dividing $270$ by $75,$ we get
Quotient $= 3,$ Remainder $=45$
$\therefore 270 = 75 × 3 + 45$
Dividing $75$ by $45,$ we get
Quotient $= 1,$ Remainder $= 30$
$\therefore 75 = 45 × 1 + 30$
Dividing $45$ by $30,$ we get
Remainder $= 15,$ Quotient $= 1$
$\therefore 45 = 30 × 1 + 15$
Dividing $30$ by $15,$ we get
Quotient $= 2,$ Remainder $= 0$
$\therefore H.C.F.$ of $1575$ and $960$ is $15$

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