Sol.
Q.
Find the largest number that will divide 445 , 572 and 699 leaving remainders 4, 5 and 6 respectively.
The required number when divides 445 , 572 and 699 leaves remainder 4 , 5 and 6.
∴
The numbers completely divisible by required number are
445 – 4 = 441,
441
441
147
49
3
3
7
7
7
1
=
×
72
32
567
189
63
3
3
3
21
3
7
7
1
567
=
×
7
34
693
231
77
3
3
7
11
11
1
693
=
×
7
×
11
32
∴
HCF of 441, 567 and 693
=
×
7
32
=
63
∴
The largest number that divides 445 , 572 and 699 leaves remainder 4, 5 and 6 is 63
572 – 5 = 567
and
699 – 6 = 693
The required number will be HCF of 441, 567 and 693