Question
Find the largest number which $615$ and $963$ leaving remainder $6$ in each case.
✓
Answer
We have to find the largest number which divides $(615 - 6)$ and $(963 - 6)$ exactly.
Therefore, the required number $= HCF$ of $609$ and $957$ Resolving $609$ and $957$ into prime factors,
we have: $609 = 3 \times 7 \times 29 957 = 3 \times 11 \times 29$
Therefore, $HCF$ of $609$ and $957$ $= 29 \times 3 = 87$
Hence, the required largest number is $87.$
Therefore, the required number $= HCF$ of $609$ and $957$ Resolving $609$ and $957$ into prime factors,
we have: $609 = 3 \times 7 \times 29 957 = 3 \times 11 \times 29$
Therefore, $HCF$ of $609$ and $957$ $= 29 \times 3 = 87$
Hence, the required largest number is $87.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The ratio of the number of male and female workers in a textile mill is $5 : 3$. If there are $115$ male workers, what is the number of female workers in the mill?
→Ramesh bought $2\frac{1}{2}\text{kg}$ sugar whereas Rohit bought $3\frac{1}{2}\text{kg}$ or sugar. Find the total amount of sugar bought by both of them.
→Tropical fruit juice is mixed from mango, papaya and orange juice in the ratio $3 : 1 : 4$. Aarushi has $400\ ml$ of orange juice. If she uses it all:
$i.\ $How many mango and papaya will he need?
$ii.\ $How much tropical fruit juice will he make altogether?
→$i.\ $How many mango and papaya will he need?
$ii.\ $How much tropical fruit juice will he make altogether?
Simplify: $2a - 3b - [3a - 2b - {a - c - (a - 2b)}]$
→Replace each $*$ by the correct digit in the following:
→Replace each $*$ by the correct digit in the following:
→Lines $p, q$ and $r$ are concurrent. Also lines $p, s$ and $t$ are concurrent. Is it always true that the lines $q, r$ and $s$ will be concurrent? Is it always true for lines $q, r$ and $t$ ?
→Consider these statements:
(a) Only the last two digits matter when deciding if a given number is divisible by 4.
(b) If the number formed by the last two digits is divisible by 4, then the original number is divisible by 4.
(c) If the original number is divisible by 4, then the number formed by the last two digits is divisible by 4.
Do you agree? Why or why not?
(a) Only the last two digits matter when deciding if a given number is divisible by 4.
(b) If the number formed by the last two digits is divisible by 4, then the original number is divisible by 4.
(c) If the original number is divisible by 4, then the number formed by the last two digits is divisible by 4.
Do you agree? Why or why not?
Kunal purchased a notebook for $Rs. 19.75$, a pencil for $Rs. 3.85$ and a pen for $Rs. 8.35$ from a bookshop. He gave a $50$ rupee note to the shopkeeper. What amount did he get back?
→Observe the pattern in the following and fill in the blanks:
$i.\ 9 \times 9 + 7 = 88$
$ii.\ 98 \times 9 + 6 = 888$
$iii.\ 987 \times 9 + 5 = 8888$
$iv.\ 9876 \times 9 + 4 =........$
$v.\ 98765 \times 9 + 3 =........$
$vi.\ 987654 \times 9 + 2 =........$
$vii.\ 9876543 \times 9 + 1 =........$
→$i.\ 9 \times 9 + 7 = 88$
$ii.\ 98 \times 9 + 6 = 888$
$iii.\ 987 \times 9 + 5 = 8888$
$iv.\ 9876 \times 9 + 4 =........$
$v.\ 98765 \times 9 + 3 =........$
$vi.\ 987654 \times 9 + 2 =........$
$vii.\ 9876543 \times 9 + 1 =........$