Find Two Numbers by Sum and HCF Calculator

Welcome to the free online calculator to find two numbers by given sum and HCF. For example, the sum of two numbers is 1215 and their HCF is 81. What are the numbers?

First, what is HCF?

HCF is short for highest common factor, which refers to the biggest number that divides more than 2 numbers without leaving a remainder. It is called by many names – greatest common factor (GCF), greatest common divisor (GCD) and highest common divisor (HCD).

Now, how to solve the problem mentioned above?

According to the question, the HCF of two numbers is 81. So, we can assume that the two numbers are 81x and 81y. Here, 81 is their HCF, x and y are positive integers and coprime.

Since the sum of two numbers is 1215, we can get the equation

81x + 81y = 1215

x + y = 121581

x + y = 15

There are 7 pairs of two positive integers that add up to 15.

(1, 14), (2, 13), (3, 12), (4, 11), (5, 10), (6, 9), (7, 8)

Among them, 4 pairs are co-prime numbers

(1, 14), (2, 13), (4, 11), (7, 8)

and 3 pairs are not co-prime numbers

(3, 12), (5, 10), (6, 9)

Next, 4 pairs of coprime multiplied by the common divisor 18. So, the two numbers are

(1 * 81, 14 * 81) = (81, 1134)

or

(2 * 81, 13 * 81) = (162, 1053)

or

(4 * 81, 11 * 81) = (324, 891)

or

(7 * 81, 8 * 81). = (567, 648)

Obviously, there is no quick way to solve such problems, all possibilities must be listed and eliminated one by one. So, we developed this free calculator to find two numbers by given sum and HCF. Omits all steps and displays the answer 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.