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Factors

# Factors of 1 | Prime Factorization of 1 | Factor Tree of 1

Written by Prerit Jain

Updated on: 05 Dec 2023

### Factors of 1 | Prime Factorization of 1 | Factor Tree of 1

Factors of a number are those which can divide the given number evenly. They leave behind no remainder. 1 is the only number that is neither prime nor composite.
All numbers have factors that are positive and negative. They also have pair factors. So, multiplying the set of two factors in pairs gives the original product. We will find the factors of 1 in this article. We will also learn about its prime factorization, and factor trees with examples. Keep reading to learn more.

## What Are the Factors of 1?

1 is the only integer out of all which is neither prime nor composite. The only factor of 1 is 1 itself. 1 is the only integer that has got only one factor and that too the number itself. In this particular blog, we will explore this fact along with several solved examples and FAQs determining the factors of 1 for you to understand better.

## What Are the Prime Factors of 1?

1 is referred to as a unit since it is the smallest possible whole number. Further, 1 is neither a prime nor a composite number that cannot be subjected to prime factorization and hence without any prime factors. Since prime factorization of 1 is not possible, because it is not a prime number hence we cannot find any prime factors of 1.

## What Are the Steps Involved in Finding the Factors of 1?

The sole factor of 1 is 1 itself. That’s it, we’re done with the 1’s factorization and hence no more factors of 1 can be calculated.

Factors may be investigated via the use of examples, interactives, and illustrations.

Factors of 10 – The factors of 10 are 1, 2, 5, and 10.
Factors of 100 – The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
Factors of 102 – The factors of 102 are 1, 2, 3, 6, 17, 34, 51, and 102.
Factors of 110 – The factors of 110 are 1, 2, 5, 10, 11, 22, 55, and 110.
Factors of 1000 – The factors of 1000 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 200, 250, 500, and 1000.

Important Points to Keep in Mind

• The only factor of 1 is the integer 1 itself.
• All the numbers known have 1 as their factor.
• Only the number 1 has both a square and a square root equal to 1.
• 1 is referred to as the identity element for multiplication which means that any number when multiplied by 1 yields the original integer.

## Find Out All the Factors of 1 in Pairs

1 can only be obtained by the product of 1 and 1, i.e., 1 = 1 × 1.
Hence, the pair factor of 1 is (1, 1).

## Solved Examples

1. Calculate the area of the square in which every side is of length 1 inch?
We find the area of the square using the formula, area = side × side = side2
According to the question, The area of the square = 1 × 1 = 1 inch square.
Hence, the area of a square having a side length of 1 inch is 1 inch2.

2. What is the common factor of 1 and 2?
1 is the only factor of 1, whereas 1 and 2 are the two common factors of the integer 2. Hence the only common factor of both the integers 1 and 2 is 1.

3. What are the two numbers with only 1 as their prime factors called?
They are called co-primes.
Co-primes are pairs of numbers with just 1 in common as a factor. In fact, the inverse is also true. Co-prime numbers are a set of two numbers where either one may be a prime or a composite.

4. How do you find the factors of 1?
For any given number, its factors are all the smaller numbers that may be evenly subdivided into it. That eliminates any components that are greater than the number we’re considering, leaving only:
0 and 1
1 divided by 1 is 1, which is a whole number, so 1 is a factor.
1 divided by 0 is infinite, which isn’t a number at all, so 0 isn’t a factor.
Thus, the only factor of 1 is 1 (itself).

Does one count as a factor?
Yes, 1 is a factor of every number.

Could 1 be a prime factor?
Since 1 is not even a prime number, therefore the answer is no, it cannot be a prime factor.

Can you tell me if 1 is a perfect square?
That’s right, 1 is the lowest perfect square number.

Which numbers are considered the prime factors of 1?
There are zero prime factors that divide into 1, hence 1 has no prime factors.

Which of the numbers 1 and X have the greatest common factor?
Since 1 is a factor of all integers, it follows that 1 is the sole factor of 1. As a result, the greatest common factor of every natural integer, as well as 1, is always 1, hence GCF(1, X) = GCF(X, 1) = 1 for all X ∈ ℕ.

Can you calculate the Sum of the Factors of 1?
Only 1 itself may be a factor of the number 1. So, the sum of the factors of 1 is always 1.

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Written by

Prerit Jain

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