The product of 3 consecutive odd numbers is 693. The largest of these numbers must be?

Question

The product of 3 consecutive odd numbers is 693. The largest of these numbers must be?

Answer 1

here's another solution

write the prime factorization of 693

693/3=231

231/3=77

77/7=11

693=3*3*7*11

(3*3)*7*11

9*7*11

7, 9, and 11 are the integers

Answer 2

Here is one way to approach this problem.  We use algebra.

 

Let the first integer = x

Let the second integer = x + 2

Let the third integer = x + 4

 

Using these variables, we can write an equation that represents the product.

 

x(x + 2)(x + 4) = 693

 

 

Solve for x from the equation.

 

x(x² + 6x + 8) = 693

x³ + 6x² + 8x = 693

 

 

Subtract 693 on both sides of the equation.

 

x³ + 6x² + 8x - 693 = 0

 

 

Solve for x from the equation.  If you never solved equations that have degrees higher than 2, here is another approach.

 

 

We try different combinations of consecutive odd integers to see which one will give us a product of 693.

 

3 * 5 * 7 = 105

 

5 * 7 * 9 = 315

 

7 * 9 * 11 = 693  ---> jackpot

 

 

The integers are 7, 9, and 11.   Out of these three integers, choose the largest one.