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