Find Two Numbers by Sum and Product Calculator

Welcome to the free online calculator to find two numbers by sum and product. For example, the sum of two numbers is 45 and their product is 500. 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 = 45

Second equation:

x * y = 500

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

x + y = 45

x = 45 – y

Substitute x = 45 - y into the second equation and simplify.

x * y = 500

(45 – y) * y = 500

45y – y² = 500

y² – 45y + 500 = 0

Now, we get a quadratic equation, the next key is to solve this quadratic equation. The answer to the quadratic equation can be calculated using the formula method or the factorization method. The factorization method is used directly here.

y² – 45y + 500 = 0

(y – 20) (y – 25) = 0

y = 20 or y = 25

When y = 20, according to the relationship between x and y, we can calculate the value of x.

x = 45 – y = 45 – 20 = 25

When y = 25, the same operation can be used to calculate x = 20.

Therefore, the two numbers are 20 and 25.

Is it right or not? Check it out!

20 + 25 = 45

20 * 25 = 500

Yes, this is correct.

Factor Method

Since the product of two numbers is 500, the two numbers must be factors of 500, a pair of factors. Therefore, we calculate the pair factors of 500 first. With the find all factors calculator, we can easily get the pair factors of 500 are

(1, 500), (2, 250), (4, 125), (5, 100), (10, 50) and (20, 25)

The next problem is simple, just find out that the sum of the pairing factors is 45.

1 + 500 = 501

2 + 250 = 252

4 + 125 = 129

5 + 100 = 105

10 + 50 = 60

20 + 25 = 45

So, we get the answer is 20 and 25.

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 sum and product. 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.