Find Two Numbers by Product and Quotient Calculator

Welcome to the free online calculator to find two numbers by product and quotient. For example, the product of two numbers is 96 and their quotient is 6. What are the numbers?

There are two methods, one is the quadratic equation method and the other is the factor method.

Quadratic Equation Method

This is the most common method. In the above example, assuming the two numbers are x and y.

Now, we can list the two equations based on the problem description.

First equation:

x * y = 96

Second equation:

xy = 6

Simplify the second equation, let x be represented by y.

xy = 6

x = 6y

Substitute x = 6y into the first equation and solve.

x * y = 96

6y * y = 96

6y² = 96

y² = 16

y = 4 or y = -4

When y = 4, according to the relationship between x and y, we can calculate the value of x.

x = 6y = 6 * 4 = 24

When y = -4, the same operation can be used to calculate x = -24.

Therefore, the two numbers are 4 and 24 or -4 and -24.

Is it right or not? Check it out!

24 * 4 = 96

24 ÷ 4 = 6

Or

(-4) * (-24) = 96

(-24) ÷ (-4) = 6

Yes, this is correct.

Factor Method

Since the product of two numbers is 96, the two numbers must be factors of 96, a pair of factors. Therefore, we calculate the pair factors of 96 first. With the find all factors calculator, we can easily get the pair factors of 96 are

(1, 96), (2, 48), (3, 32), (4, 24), (6, 16) and (8, 12)

The next problem is simple, just find out that the quotient of the pairing factors is 6. Obviously, (4, 24) satisfy the condition. So, the two numbers are 4 and 24.

This method only calculates positive integers and ignores negative values. If necessary, add a negative sign in front of positive integers.

Well, these are two common solutions that, while simple, both require a certain amount of calculation. So, we developed this free calculator to find two numbers by product and quotient. No calculations required and answers in milliseconds.

Next, we will introduce how to use the calculator.

Using the calculator is simple, follow these 3 steps:

Next, let’s look at some examples.