MCQ
The largest number which divides $245$ and $1029$ leaving remainder $5$ in each case is :
- A$12$
- ✓$16$
- C$8$
- D$4$
✓
Answer
Correct option: B.
$16$
Let us subtract $5 \ ($the remainder$)$ from each number in order to find their $\text{HCF}$.
$245 - 5 = 240$
$1029 - 5 = 1024$
Now, Let us find $\text{HCF}$ of $240, 1024$
$1024 = 240 × 4 + 64$
$240 = 64 × 3 + 48$
$64 = 48 × 1 + 16$
$48 = 16 × 3 + 0$
The largest number which divides $245$ and $1029$ leaving remainder $5$ in each case is $16$.
$245 - 5 = 240$
$1029 - 5 = 1024$
Now, Let us find $\text{HCF}$ of $240, 1024$
$1024 = 240 × 4 + 64$
$240 = 64 × 3 + 48$
$64 = 48 × 1 + 16$
$48 = 16 × 3 + 0$
The largest number which divides $245$ and $1029$ leaving remainder $5$ in each case is $16$.
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