For this we first need to find the square root of 5607 by division method .
there will be a remainder . We need to subtract that reminder from 5607 to get a perfe t square number. Then we need to find the square root of it.

Introduction:
To find the least number that must be subtracted from 5607 to get a perfect square, we need to consider the factors of 5607 and find the closest perfect square.

Factors of 5607:
To find the factors of 5607, we can start by dividing it by the smallest prime number, which is 2. If 2 is a factor, we can divide it again by 2 until we can no longer divide evenly. Then, we move on to the next prime number, which is 3, and repeat the process. This is known as prime factorization.

Prime factorization of 5607:
5607 ÷ 3 = 1869
1869 ÷ 3 = 623
623 ÷ 7 = 89

Therefore, the prime factorization of 5607 is 3 × 3 × 7 × 89.

Perfect Square:
To determine the perfect square closest to 5607, we need to find the square root of each prime factor and multiply them.

Square root of 3: √3 ≈ 1.732
Square root of 7: √7 ≈ 2.646
Square root of 89: √89 ≈ 9.434

The square root of 5607 can be approximated by multiplying the square roots of its prime factors:
√5607 ≈ √(3 × 3 × 7 × 89) ≈ (1.732 × 2.646 × 9.434) ≈ 45.865

The closest perfect square to 5607 is 46^2 = 2116.

Calculating the Least Number:
To find the least number that must be subtracted from 5607 to get a perfect square, we subtract the closest perfect square from 5607.

5607 - 2116 = 3491

Therefore, the least number that must be subtracted from 5607 to get a perfect square is 3491.

Summary:
To find the least number that must be subtracted from 5607 to get a perfect square, we determined the prime factorization of 5607 and found the closest perfect square by multiplying the square roots of its prime factors. The closest perfect square to 5607 is 2116, and subtracting it from 5607 gives us the least number of 3491.