Question

define HCF of two positive integer and find HCF of 475 and 495​

Answer 1

Answer:

HCF (highest common factor) :  

The largest positive integer that divides given two positive integers is called the Highest Common Factor of these positive integers.

Step-by-step explanation:

(v) Given : Two positive integers  475 and 495.

Here, 495 > 475

Let a = 495 and b = 475

495 = 475 x 1 + 20.

[By applying division lemma, a = bq + r]

Here, remainder = 20 ≠ 0, so take new dividend as 475 and new divisor as 20.

Let a = 474 and b= 20

475 = 20 x 23 + 15.

Here, remainder = 15 ≠ 0, so take new dividend as 20 and new divisor as 15.

Let a = 20 and b= 15

20 = 15 x 1 + 5.

Here, remainder = 5 ≠ 0, so take new dividend as 15 and new divisor as 5.

Let a = 15 and b= 5

15 = 5 x 3+ 0.

Here, remainder is zero and divisor is 5.

Hence ,H.C.F. of 475 and 495 is 5

(vi) Given : Two positive integers  75 and 243.

Here, 75 > 243

Let a = 75 and b = 243

243 = 75 x 3 + 18.

[By applying division lemma, a = bq + r]

Here, remainder = 18 ≠ 0, so take new dividend as 75 and new divisor as 18.

Let a = 75 and b= 18

75 = 18 x 4 + 3.

Here, remainder = 3 ≠ 0, so take new dividend as 18 and new divisor as 3.

Let a = 18 and b= 3

18 = 3 x 6+ 0.

Here, remainder is zero and divisor is 3..

Hence ,H.C.F. of 75 and 243 is 3.

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Answer 2

$\huge\fbox \red{Solution:}$

$\fbox \blue{By applying Euclid’s Division lemma on 495 and 475 we get,}$

495 = 475 x 1 + 20.

Since remainder ≠ 0, apply division lemma on 475 and remainder 20

475 = 20 x 23 + 15.

Since remainder ≠ 0, apply division lemma on 20 and remainder 15

20 = 15 x 1 + 5.

Since remainder ≠ 0, apply division lemma on 15 and remainder 5

15 = 5 x 3+ 0.

$\fbox \blue{Therefore, H.C.F. of 475 and 495 is 5}$

$\rm\orange{Thanks}$