Question

By what number should 1365 be divided to get 31 as question and32 as remainder

Answer 1

Answer:

43

Step-by-step explanation:

Dividend = 1365

Quotient = 31

Remainder = 32

Divisor = ?

Let divisor be x

By the division algorithm,

Dividend = (Divisor × Quotient) + Remainder

1365 = (x × 31) + 32

1333 = x × 31

x       = 43

Ans: 1365 must be divided by 43 to get quotient as 31 and remainder as 32.

Answer 2

Given :-

• Dividend (a) = 1365

• Quotient (q) = 31

• Remainder (r) = 32

To find :-

• Divisor = ?

Solution :-

Let the divisor be b

we know that,

Dividend = Divisor × quotient + remainder

or,

$\orange{\bigstar}\:\:{\underline{\boxed{\bf\pink{a=bq+r}}}}$

$\rm\longrightarrow\:3165=b\times{31}+32$

$\rm\longrightarrow\:3165=31b+32$

$\rm\longrightarrow\:3165-32=31b$

$\rm\longrightarrow\:1333=31b$

$\rm\longrightarrow\cancel\dfrac{1333}{31}=b$

$\rm\longrightarrow\:43=b$

$\rm\longrightarrow\:b=43$

Hence,1365 should be divided by 43 to get 31 as quotient and 32 as remainder.

More Information :-

Euclid's division algorithm :-

➝ If any two given positive integers a and b there exist unique whole numbers q and r such that,

• a = bq + r where 0 ≤ r < b.

• Dividend (a)
• divisor (b)
• quotient (q)
• remainder (r)