Q. 34.0( 23 Votes )

Find the HCF of t

Answer :

(i) Using Euclid’s Division Lemma


a = bq + r, (o ≤r<b)


963 = 657×1 + 306


657 = 306×2 + 45


306 = 45×6+36


45 = 36×1+9


36 = 9×4+0


∴ HCF (657, 963) = 9


linear form:
657a + 306b = 9
The above equation have many solutions, one of them is a = -15, b = 22
i.e. 9 = 657(-15) + 306(22) 

(ii) Using Euclid’s Division Lemma


a = bq + r, (o ≤r<b)


592 = 252×2+88


252 = 88×2+76


88 = 76×1+12


76 = 12×6+4


12 = 4×3+0


∴ HCF (592, 252) = 4

linear form:
592a + 252b = 4
The above equation have many solutions, one of them is a = 77, b = -20
i.e. 4 = 592(77) + 252(20) 

(iii) Using Euclid’s Division Lemma


a = bq + r, (o ≤r<b)


1155 = 506×2+143


506 = 143×3+77


143 = 77×1+66


77 = 66×1+11


66 = 11×6+0


∴ HCF (506, 1155) = 11

linear form:
506a + 1155b = 11
The above equation have many solutions, one of them is a = 16, b = -7
i.e. 11 = 506(16) + 1155(-7) 

(iv) Using Euclid’s Division Lemma


a = bq + r, (o ≤r<b)


1288 = 575×2+138


575 = 138×4+23


138 = 23×6+0


∴ HCF (1288, 575) = 23

linear form:
1288a + 575b = 23
The above equation have many solutions, one of them is a = 4, b = 9
i.e. 23 = 1288(4) + 575(9) 

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