Question

find the smallest number by which 10,985 should be divided so that the quotient is a perfect square​

Answer 1

Answer:

5| 10985

13| 2197

13| 169

13| 13

Answer 2

Note:

"Prime Factorisation" is a method of writing a number as a product of its prime numbers.

A perfect square is a integer that is a square of another integer.

Write 10985 as a product of its prime factors:

$10985 = 5 \times 13 \times 13 \times 13$

$10985 = 5 \times 13^3$

Find the number to divide so that the quotient is a perfect square:

$\text {Perfect Square} = 13^2, \text {therefore, we do not want 5 and 13}$

$\text {Divisor} = 5 \times 13$

$\text {Divisor} =65$

Check:

$\text{Quotient } = 10985 \div 65$

$\text{Quotient } = 169$

$169 \text { is a perfect square, because},169 = 13^2$

Answer: 65