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# Elements of 17 | The best way to Discover the Elements of 17 by Division Technique?

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The elements of 17 are the numbers that divide 17 precisely with out leaving any the rest. As 17 is a chief quantity, it has solely two elements. The pair elements of 17 might be constructive or adverse. For instance, the pair issue of 17 might be (1, 17) or (-1, -17). If we multiply the pair of adverse numbers, similar to multiplying -1 and -17, it should end result within the unique quantity 17. Right here, we’ll study what are the elements of 17, pair elements and the prime elements of 17 utilizing the prime factorization technique and plenty of solved examples.

Desk of Contents:

• What are the Elements of 17?
• Pair Elements of 17
• Elements of 17 by Division Technique
• Prime Factorization of 17
• Solved Examples
• FAQs

## What are the Elements of 17?

The numbers that divide 17 utterly and go away the rest 0, then the numbers are the elements of 17. In different phrases, if two numbers are multiplied collectively and lead to 17, then the numbers are the elements of 17. As 17 is a chief quantity, it has solely two elements, similar to 1 and the quantity itself. Therefore, the elements of 17 are 1 and 17.

## Pair Elements of 17

A pair of numbers which can be multiplied collectively and leading to 17, then it’s known as the pair issue of 17. We all know that 17 is a chief quantity and it has one constructive pair issue and one adverse pair issue. The constructive and adverse pair elements of 17 are given beneath:

Constructive Pair Issue of 17:

Detrimental Pair Issue of 17:

Due to this fact, the constructive and adverse pair elements of 17 are (1, 17) and (-1, -17) respectively.

## Elements of 17 by Division Technique

Within the division technique, the elements of 17 are discovered by dividing 17 by completely different integers. If the integers divide 17 utterly with out leaving any the rest, then these integers are the elements of 17. Now, allow us to talk about find out how to discover the elements of 17 by division technique.

Now, let’s begin dividing 17 by 1 and proceed with the opposite integers.

• 17/1 = 17 (Issue is 1 and The rest is 0)
• 17/17 = 1 (Issue is 17 and The rest is 0)

If we divide 17 by any numbers aside from 1 and 17, it leaves a the rest worth. Therefore, the elements of 17 are 1 and 17.

## Prime Factorization of 17

Within the prime factorization of 17, the quantity 17 is written because the product of its prime elements. Thus, the method of discovering the prime elements of 17 is given beneath.

Now, take the pair issue of 17, say (1, 17)

Now, verify whether or not the numbers within the pair elements are prime numbers or composite numbers. If a quantity is a chief quantity, go away the quantity as it’s. In case, if the numbers within the pair issue are composite numbers, break up the numbers into their prime elements, and write these numbers because the product of its prime elements.

We all know that the number one is neither prime nor composite and therefore it can’t break up additional.

Now, take the opposite quantity 17, which can be a chief quantity.

Therefore, 17 is written because the product of 1 and 17.

(i.e.) 17 = 1 × 17.

Due to this fact, the prime factorization of 17 is 17 or 171.

## Solved Examples

Instance 1:

Discover the widespread elements of 17 and 16.

Resolution:

The elements of 17 are 1 and 17.

The elements of 16 are 1, 2, 4, 8 and 16.

Thus, the widespread issue of 17 and 16 is 1.

Instance 2:

Discover the widespread elements of 17 and 18.

Resolution:

Elements of 17 = 1 and 17

Elements of 18 = 1, 2, 3, 6, 9 and 18.

As 17 is a chief quantity, the widespread issue of 17 and 18 is 1.

Instance 3:

Discover the widespread elements of 17 and 11.

Resolution:

The elements of 17 are 1 and 17.

The elements of 11 are 1 and 11.

As each the numbers 17 and 11 are prime numbers, the widespread issue of 17 and 11 is 1.

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