Question

what is the hcf of 960and 1575 sing euclid division algorithm

Answer 1

Step 1:-

1575 = 960 × 1 + 615

Step 2 :-

960 = 615 × 1 + 345

Step 3 :-

615 = 345 × 1 + 270

Step 4 :-

345 = 270 × 1 + 75

Step 5 :-

270 = 75 × 3 + 45

Step 6 :-

75 = 45 × 1 + 30

Step 7 :-

45 = 30 × 1 + 15

Step 8 :-

30 = 15 × 2 + 0

Remainder = 0

So,

HCF ( 960, 1575) = 15

Answer 2

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___ Euclid's division Algorithm ____

Apply Euclid's division lemma
a = b × q + r
Dividend = Divisor × Quotient + Remainder

Here, Q . is given Find the H.C.F of 960 and 1575 .

Sol. ...

-step :1. since 1575 > 960 .
we apply the division lemma to 1575 and 960 to get,

=> 1576 = 960 × 1 + 615

=> 960 = 615 × 1 + 345

=> 615 = 345 × 1 + 270

=> 345 = 270 × 1 + 75

=> 270 = 75 × 3 + 45

=> 75 = 45 × 1 + 30

=> 45 = 30 × 1 + 15

=> 30 = 15 × 2 + 0

The remainder has now become zero, so our procedure stops.
since, the Divisor at this step is 15 .

The H.C.F of 960 and 1575 is 15


ANS- 15