1008 divided by which digit number gives a perfect square?

To find a digit number that divides 1008 to yield a perfect square, we first need to factor 1008.

Factoring 1008

The prime factorization of 1008 is:

• 1008 = 2^4 × 3^2 × 7

Understanding Perfect Squares

A perfect square has all prime factors raised to even powers. Therefore, we need to adjust the powers of the factors in 1008.

Finding Suitable Divisors

We can divide 1008 by the following digit numbers (1-9) to check for perfect squares:

• 1: 1008 / 1 = 1008 (not a perfect square)
• 2: 1008 / 2 = 504 (not a perfect square)
• 3: 1008 / 3 = 336 (not a perfect square)
• 4: 1008 / 4 = 252 (not a perfect square)
• 6: 1008 / 6 = 168 (not a perfect square)
• 7: 1008 / 7 = 144 (which is 12^2, a perfect square)
• 8: 1008 / 8 = 126 (not a perfect square)
• 9: 1008 / 9 = 112 (not a perfect square)

Conclusion

The digit number that divides 1008 to give a perfect square is 7, resulting in 144, which is a perfect square (12 x 12).