Find Two Numbers by Product and HCF Calculator

Welcome to the free online calculator to find two numbers by given product and HCF. For example, the product of two numbers is 2028 and their HCF is 13. 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?

There are two methods, one is the assumption method and the other is the factor pair method.

Method 1: Assumption method

According to the question, the HCF of two numbers is 13. So, we can assume that the two numbers are 13x and 13y. x and y are positive integers and coprime.

Since the product of them is 2028, we can get equation

13x * 13y = 2028

169xy = 2028

xy = 12

There are 3 pairs of two positive integers whose product is 12.

(1, 12), (2, 6), (3, 4)

Among them, 2 pairs are co-prime numbers

(1, 12), (3, 4)

and 1 pair is not co-prime numbers

(2, 6)

So, the two numbers are (13 * 1 = 13, 13 * 12 = 156) or (13 * 3 = 39, 13 * 4 = 52).

Let’s verify.

13 * 156 = 2028

HCF(13, 156) = 13

Or

39 * 52 = 2028

HCF(39, 52) = 13

Correct.

Method 2: Factor pair method

Because the product of two numbers is 2028. So, these two numbers must be factors of 2028, a pair of factors.

Therefore, we can calculate the pair factors of 2028 first. Then, find the pair of factors whose HCF is 13.

With the find all factors calculator, we can easily get the pair factors of 2028 are

(1, 2028), (2, 1014), (3, 676), (4, 507), (6, 338), (12, 169), (13, 156), (26, 78) and (39, 52)

The next problem is simple, just find out that the HCF of the pairing factors is 13.

HCF(1, 2028) = 1

HCF(2, 1014) = 2

HCF(3, 676) = 1

HCF(4, 507) = 1

HCF(6, 338) = 2

HCF(12, 169) = 1

HCF(13, 156) = 13

HCF(26, 78) = 26

HCF(39, 52) = 13

So, we can also get the answer is (13, 156) and (39, 52).

Well, these are two common solutions that, each method requires a detailed discussion. So, we developed this free calculator to find two numbers by given product and HCF. No discussions required 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.