How to Find 2 Consecutive Integers Whose Product is 272?

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The product of 2 consecutive integers is 272, what are these 2 integers? The answer are 16 and 17. How to find these 2 consecutive integers whose product is 272? Here are three methods, especially the third method, which can be easily calculated without the help of other tools. Let’s introduce them one by one.

How to find 2 consecutive integers whose product is 272?

Method 1: Assumption Method

This is a common mathematical solution. Assuming that N is used to represent the first integer, so the second integer is N + 1.

Now, the product of 2 consecutive integers is 272, which can be expressed by equation

N * (N + 1) = 272

Solving equations

N * (N + 1) = 272

N2 + N = 272

N2 + N – 272 = 0

(N – 16) * (N + 17) = 0

N = 16 or N = -17

You can see that the first integer has 2 values 16 and -17. So, The second integer also has two values, 17 and -16.

Let’s verify whether the answer is correct?

The first set 16 and 17.

16 * 17 = 272. Correct.

Then let’s verify the second set of answers -17 and -16.

-17 * -16 = 272. This is also eligible.

So, there are two answers of 2 consecutive integers whose product is 272, one set is 16 and 17, the other set is -17 and -16.

The key to this method is to solve the quadratic equation. If you are not familiar with quadratic equations, the second or third method is recommended. Now we will introduce the second method.

Method 2: Root Sign Method

According to the definition of the root sign, if An = B, then A is the nth root of B to the nth power. An is the multiplication of n identical A.

Now, we need to find 2 consecutive integers whose product is 272, which can be regarded as the product of 2 identical numbers is 272. That is, find the 2nd root of 272. As long as we find this number, we can use this number as the fulcrum to find the consecutive integers that meet the conditions.

The equation is as follows

A2 = 272

With the help of the root calculator, you can easily calculate A = 16.49, round down to an integer A = 16.

The product of 2 consecutive integers is 272, one integer is 16, the other integer is 272 / 16 = 17.

16 and 17 are just two adjacent integers, which meet the requirements.

16 and 17 are positive integers. If their negative integers are taken, will their product be 272?

-17 * -16 = 272.

Yes, -17 and -16 are also the answer of 2 consecutive integers whose product is 272.

So, there are two answers of 2 consecutive integers whose product is 272, one set is 16 and 17, the other set is -17 and -16. The result is the same as the first method.

Obviously, this method needs to calculate the 2nd root first. If you can’t calculate the 2nd root manually, you need to use a root calculator to calculate it. What if there is no such auxiliary tool? It doesn’t matter, let’s move on to the third method.

Method 3: Divisor Method

First of all, we must understand what is divisor. The divisor is also called a factor. If A is divisible by B, B is called A divisor.

Obviously, the product of 2 consecutive integers is 272, so these 2 consecutive integers are all divisors of 272. How to find these divisor numbers? First, decompose 272 with the smallest divisor more than 1, and then decompose the obtained quotient until the quotient can no longer be decomposed. Note that the indecomposable here means that no other divisor can be found except 1 and itself. This means that the final quotient is a prime number.

Back to the question: find 2 consecutive integers whose product is 272.

  • The first step, decompose 272 by the smallest divisor except 1. 272 / 2 = 136;
  • The second step, 136 is decomposed by the smallest divisor except 1. 136 / 2 = 68;
  • The third step, 68 is decomposed by the smallest divisor except 1. 68 / 2 = 34;

By analogy, the following equation is obtained

272
= 2 * 136
= 2 * 2 * 68
= 2 * 2 * 2 * 34
= 2 * 2 * 2 * 2 * 17

Next, group the obtained divisors. Here, you need to divide the last row of numbers 2 * 2 * 2 * 2 * 17 into 2 groups. Obviously, one group is 17, the other group is 2 * 2 * 2 * 2 = 16.

So, 16 and 17 are the answer of 2 consecutive integers whose product is 272.

As with the second method, discuss the negative numbers to get another answer -17 and -16.

Is not it simple? The whole process does not require any tools at all. Of course, if you have any questions about the grouping process, please refer to another article Consecutive Integers Calculator Based On A Given Product

FAQS

Now, we have found that the product of 2 consecutive integers is 272, some problems can be solved by the way.

  • 1. What are two consecutive integers whose product is 272?
    There are two answers of two consecutive integers whose product is 272, one set is 16 and 17, the other set is -17 and -16.
  • 2. What is the smaller of two consecutive integers whose product is 272?
    The smaller positive integer is 16. The smaller negative integer is -17.
  • 3. What is the greater of two consecutive integers whose product is 272?
    The greater positive integer is 17. The greater negative integer is -16.
  • 4. What is the average of two consecutive positive integers whose product is 272?
    The average of these 2 consecutive positive integers is (16 + 17) / 2 = 33 / 2 = 16.5.
  • 5. What is the sum of two consecutive positive integers whose product is 272?
    The product of 2 consecutive positive integers is 272, the sum of them is 16 + 17 = 33.
  • 6. What is the sum of square of two consecutive positive integers whose product is 272?
    The product of 2 consecutive integers is 272, the sum of their squares is 162 + 172 = 545.

Conclusion

The above provides three methods to find 2 consecutive integers whose product is 272. To rank these three methods, I still like the third method. Although the steps are a bit long, the overall calculation difficulty is very small, which is very suitable for a manual calculation. The second method is suitable for those with a root calculator.

In addition, there is one of the easiest way: directly use the calculator provided on this page to find 2 consecutive integers based on the product. It can eliminate all calculation steps and get the answer directly, which is very convenient and suitable for everyone!

Of course, if the number of consecutive integers you want to calculate is not 2, or if you need to calculate consecutive odd integers or even integers. It is recommended to use our more advanced product-based consecutive integers calculator, where you can specify the number of integers and Integer type. I believe it can meet your requirements.

Well, the above is all about finding 2 consecutive integers whose product is 272. Please leave a message and tell me, which one of the three methods do you like?

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