Find Two Consecutive Multiples by Their Product Calculator

Welcome to the free online calculator to find two consecutive multiples by their product. For example, the product of two consecutive multiples of 5 is 1050, what are the two consecutive multiples?

What is a multiple? If an integer a is divisible by b, then a is a multiple of b.

Consecutive multiples are consecutive numbers multiplied by the same multiple.

For example, the consecutive numbers 3, 4, 5 and 6 multiplied by 8 are 24, 32, 40 and 48. So, 24, 32, 40 and 48 are consecutive multiples of 8.

Now, how to calculate two consecutive multiples by their product?

By the example at the beginning, the product of two consecutive multiples of 5 is 1050, what are the two consecutive multiples?

Let these two consecutive numbers be x and x + 1.

Multiply by 5, it is 2 consecutive multiples of 5.

5x, 5(x + 1)

Because the product of them is 1050, so we can get an equation

5x * 5(x + 1) = 1050

Simplify and solve.

5x * 5(x + 1) = 1050

5x * (5x + 5) = 1050

25x² + 25x = 1050

x² + x = 42

x² + x – 42 = 0

(x – 6) (x + 7) = 0

x = 6 or x = -7

So, these two consecutive numbers are (6, 7) or (-7, -6). Their multiples of 5 are (30, 35) or (-35, -30).

Verify

30 * 35 = 1050

Or

(-35) * (-30) = 1050

Correct.

Method 2: Factor Pairs method

Because the product of two consecutive multiples of 5 is 1050. So, these two consecutive multiples must be factors of 1050, a pair of factors.

Therefore, we can calculate the factor pairs of 1050 first. Then, find the pair of factors that are multiples of 5.

With the find all factors calculator, we can easily get the factor pairs of 1050 are

(1, 1050), (2, 525), (3, 350), (5, 210), (6, 175), (7, 150), (10, 105), (14, 75), (15, 70), (21, 50), (25, 42), (30, 35)

Next, find factor pairs that are multiples of 5.

(5, 210), (10, 105), (15, 70), (30, 35)

Finally, check if they are consecutive multiples of 5. This means that the difference between them is 5.

210 – 5 = 205

105 – 10 = 95

70 – 15 = 55

35 – 30 = 5

So, we get two positive consecutive multiples of 5 are 30 and 35, and their product is 1050.

By the way, check whether the form of negative numbers is OK.

(-30) * (-35) = 1050

Obviously, -30 and -35 are also possible.

In summary, the two consecutive multiples of 5 are (30, 35) or (-30, -35).

Of course, there are other solutions, depending on your knowledge base. If you don’t want to calculate by hand, it is recommended to use the Find Two Consecutive Multiples by Their Product Calculator on the page directly, enter the number and you can get the answer immediately.

Next, we will introduce how to use the calculator.

Using the calculator is simple, follow these 4 steps:

Next, let’s look at some examples.