Page 27 - classs 6 a_Neat

EXAMPLE 9: Find the HCF of 161 and 345 by the division method. EXAMPLE 12: Find the greatest number which divides 285 and 1249, leaving remainders 9 and 7
SOLUTION: Method respectively.
161 345 2
- 322 SOLUTION: Clearly, we must find the greatest number which divides (285 - 9) and (1249 - 7)
23 161 7 exactly.
- 161 So, the required number= HCF of 276 and 1242.
× 276 1242 4
- 1104
138 276 2

Hence, the HCF of 161 and 345 is 23. - 276
×
EXAMPLE 10: Find the HCF of 513 and 783. Hence, the required number= 138.
SOLUTION: By the division method, we have

513 783 1 EXAMPLE 13: Reduce 289 to the lowest terms.
- 531 391
270 513 1 SOLUTION: For reducing the given fraction to the lowest terms, we divide its numerator and the
- 270 denominator by their HCF.
243 270 1 Now, we find the HCF of 289 and 391 as under:
- 243 289 391 4
27 243 9 - 289
- 243 102 289 2
× - 204

Hence, the HCF of 513 and 783 is 27. 85 102 1
- 85
TO FIND THE HCF OF MORE THAN TWO NUMBERS if more than two numbers are given, choose any 17 85 5
two ofthemandfind their HCF. The HCFofthis HCFand the third number gives the HCFof these three numbers.
The HCF of this HCF and the fourth number gives the HCF of these four number and so on. - 85
×
EXAMPLE 11: Find the on. HCF of 136,170 and 25 Hence, the HCF of 289 and 391 is 17.
SOLUTION: First we find the HCF of 136 and 170 Now, dividing the numerator and the denominator of the given fraction by 17, we get :
136 170 1 289 = 289 ÷ 17 = 17

- 136 391 391 ÷ 17 23.
34 136 1
- 136
×
Thus the HCF of 136 and 170 is 34.
Now, we fing the HCF of 34 and 255.
34 255 7
238
17 34 2
- 34
×
So, the HCF of 34 and 255 is 17.
Hence, the HCF of 136, 170 and 255 is 17.