Diamond Problem Solver

Created By : Veerendra
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Oct 21,2023

Solving Diamond Problems isn't going to be tough anymore with our Diamond Problem Solver. You just need to fill any two integers as the input data and tap on the calculate button to know the rest two in a matter of seconds. You can use diamond math problem calculator or diamond problems calculator, and diamond puzzle solver for further extent in the same concept through one hit on the calculate button with some inputs.

Diamond Problem Solver
Factor A
Factor B

Diamond Problem Solver: If you are searching for a handy tool that does the calculations of Diamond Problems at a faster pace you have come to the right destination. This user-friendly tool allows you to enter two numbers and find the rest two easily. By referring to the further modules you will learn on what a diamond problem is and how to solve different diamond problems of various kinds. Make use of the solved examples provided to get a grip on the concept.

How to do Diamond Problems?

There are three major cases, that you will have while solving Diamond Problems. All of them are listed below and along with how to approach them with a neat explanation. Follow the steps and find the results in an effective manner. They are as under

  • Given Two Factors
  • Given One Factor and the Product or Sum
  • Given Product and Sum

Case 1: Given Two Factors

Of all the cases this is the easiest one and you will have two numbers A and B for which you need to find the Sum and Product.

  • Calculate the Product of numbers by simply multiplying them and write it on the top of the cross or diamond shape.
  • Perform Addition Operation of given numbers to get the Sum and place it on the bottom of the diamond. Let's see diamond math problems

Question: Calculate the Product and Sum if you know the two factors 13, 4?


Given Factors are 13, 4

Product = 13*4 = 52

Sum = 13+4 = 17

Case 2: Given One Factor and the Product or Sum

This is slightly complicated compared to the earlier one where you will have one factor and product or sum.

Factor A + Factor B = Sum

Factor B = Sum - Factor A

Knowing both the factors finding the Product is relatively easy as you can perform basic multiplication.

Factor A * Factor B = Product

Factor B = Product/Factor A

After obtaining the second factor find the last missing term i.e. Sum easily by adding both the factors.

  • Firstly try finding the other factor.
  • Later transform your equation in a way that you can solve the unknown value.
  • a) If you have a factor and sum you can find the other factor through a simple subtraction.
  • b) If you have a factor and product divide the product with the factor in order to get the second factor.

Question: Find the other factor and sum if one of the factor is  7 and product is 63?


Factor A * Factor B = Product

7*Factor B = 63

Factor B = 63/7 = 9

Sum = Factor A + Factor B

= 7+9


Case 3: Given Product and Sum

This is the last case and the most common diamond problem. In this case, you will know the product and sum but doesn't know the numbers itself. These kind of problems are helpful when you are learning about factoring.

  • List out all the possible pairs that will give the product.
  • Sum these two numbers and check for which combination gives the desired sum.
  • You can stop after the sum and product meet the condition.

Question: Find the Factors if the Product and Sum are given as 12 and 7?


Product = 12

Sum = 7

Possible pairs that result in the product 12 are

12 = 1 * 12

12 = 2 * 6

12 = 3 * 4

Don't forget the negative numbers:

12 = -1 * -12

12 = -2 * -6

12 = -3 * -4

Step 2: Sum these numbers and check which combination meets the desired sum

1+12 = 13

2+6 = 8

3+4 = 7

In all the cases, the numbers that meets the condition are 3 and 4.

Therefore, 3 and 4 are the required factors whose product is 12 and sum is 7.

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FAQs on Diamond Problem Solver

1. How to do a Diamond Problem using Tools?

Just enter the two numbers as inputs and hit on the calculate button to find the rest two easily.

2. What are the Criterias supported by this Diamond Problem Tools?

Diamond Problem Solver supports three different conditions if Two Factors, One Factor and the Product or Sum, Product and Sum are given. You can find the rest two easily.

3. Where do I get the Step by Step Procedure for solving Diamond Problems?

You can get the Step by Step Procedure for solving Diamond Problems on our page.

4. What is the Product and Sum if the factors are 12 and 5?

Product = 12 *5 = 60

Sum = 12+5 = 17