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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

Contents

1Factors of 12Factors of 23Factors of 34Factors of 45Factors of 56Factors of 67Factors of 78Factors of 89Factors of 910Factors of 1011Factors of 1112Factors of 1213Factors of 1314Factors of 1415Factors of 1516Factors of 1617Factors of 1718Factors of 1819Factors of 1920Factors of 2021Factors of 2122Factors of 2223Factors of 2324Factors of 2425Factors of 2526Factors of 2627Factors of 2728Factors of 2829Factors of 2930Factors of 3031Factors of 3132Factors of 3233Factors of 3334Factors of 3435Factors of 3536Factors of 3637Factors of 3738Factors of 3839Factors of 3940Factors of 4041Factors of 4142Factors of 4243Factors of 4344Factors of 4445Factors of 4546Factors of 4647Factors of 4748Factors of 4849Factors of 4950Factors of 5051Factors of 5152Factors of 5253Factors of 5354Factors of 5455Factors of 5556Factors of 5657Factors of 5758Factors of 5859Factors of 5960Factors of 6061Factors of 6162Factors of 6263Factors of 6364Factors of 6465Factors of 6566Factors of 6667Factors of 6768Factors of 6869Factors of 6970Factors of 7071Factors of 7172Factors of 7273Factors of 7474Factors of 7575Factors of 7676Factors of 7777Factors of 7878Factors of 7979Factors of 8080Factors of 8181Factors of 8282Factors of 8383Factors of 8484Factors of 8585Factors of 8686Factors of 8787Factors of 8888Factors of 8989Factors of 9090Factors of 9191Factors of 9292Factors of 9493Factors of 9694Factors of 9795Factors of 9896Factors of 9997Factors of 10098Factors of 10199Factors of 102100Factors of 103101Factors of 104102Factors of 105103Factors of 106104Factors of 107105Factors of 108106Factors of 109107Factors of 110108Factors of 111109Factors of 112110Factors of 113111Factors of 114112Factors of 115113Factors of 116114Factors of 117115Factors of 118116Factors of 119117Factors of 120118Factors of 122119Factors of 123120Factors of 124121Factors of 125122Factors of 126123Factors of 127124Factors of 128125Factors of 129126Factors of 130127Factors of 131128Factors of 132129Factors of 133130Factors of 134131Factors of 135132Factors of 136133Factors of 137134Factors of 138135Factors of 139136Factors of 140137Factors of 141138Factors of 142139Factors of 143140Factors of 144141Factors of 145142Factors of 146143Factors of 147144Factors of 148145Factors of 149146Factors of 150147Factors of 151148Factors of 152149Factors of 153150Factors of 154151Factors of 155152Factors of 156153Factors of 157154Factors of 158155Factors of 159156Factors of 160157Factors of 161158Factors of 162159Factors of 163160Factors of 167161Factors of 168162Factors of 169163Factors of 170164Factors of 172165Factors of 174166Factors of 176167Factors of 178168Factors of 180169Factors of 182170Factors of 184171Factors of 186172Factors of 188173Factors of 190174Factors of 192175Factors of 194176Factors of 196177Factors of 197178Factors of 200179Factors of 215180Factors of 216181Factors of 415
Factors of 1 | Prime Factorization of 1 | Factor Tree of 1

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.

The factor of 1: 1 
Negative Factor of 1: -1
Prime Factorization of 1: Since 1 has no prime factors, hence it cannot be prime factorized.
Sum of Factors of 1: 1

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).

Frequently Asked Questions

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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