Hope this Factor Tree of ours guide will be useful to you. Here we (FactorTree.Blog) have analyzed the different factors in a very simple way.

Factors of 1 | Factor Tree of 1

Today we are going to present here Factor Tree of 1. The factor is the number that divides the original number. 1 is neither a prime number nor a composite number. The factors of 1 is one itself.

factor-tree-of-1

Now, let's apply our understanding of factors to our special number 1.

What number (or numbers) can divide 1 perfectly, leaving no remainder?

The Answer is If you try to divide 1 by any number other than 1 itself (e.g., 1 divided by 2, 1 divided by 3), you'll always get a fraction or a decimal. The only number that divides 1 perfectly is 1 itself.

The only factor of the number 1 is 1. It's the only number that has just one factor. This makes 1 truly unique in the world of numbers!

One Neither Prime Nor Composite

Prime Numbers: A prime number is a natural number greater than 1 that has exactly two distinct factors: 1 and itself.

Examples: 2 (factors: 1, 2), 3 (factors: 1, 3), 5 (factors: 1, 5), 7 (factors: 1, 7).

Composite Numbers: A composite number is a natural number greater than 1 that has more than two factors.

Examples: 4 (factors: 1, 2, 4), 6 (factors: 1, 2, 3, 6), 9 (factors: 1, 3, 9).

Where Does '1' Stand?

Since 1 has only one factor (which is 1 itself), it doesn't fit the definition of a prime number (which requires two distinct factors).

It also doesn't fit the definition of a composite number (which requires more than two factors).

Conclusion for factorization 1:

  • The number 1 is neither a prime number nor a composite number.
  • It's a special category all its own!
  • This unique status highlights its fundamental role as the 'multiplicative identity' – any number multiplied by 1 remains unchanged (e.g., 5 x 1 = 5, 100 x 1 = 100).

Factorization of 1

Imagine a bustling Indian family gathering – there are grandparents, parents, children, cousins. Each person is a unique individual. Now, imagine a single, solitary individual standing apart. That's a bit like the number 1 in the world of numbers. It's often overlooked because of its apparent simplicity, but its role is profoundly significant.

Why 1 is NOT Prime?

A prime number must be greater than 1.

A prime number must have exactly two distinct positive factors (1 and itself). The number 1 only has one positive factor (which is 1).

Since 1 is not prime, and it doesn't have any prime factors (because it's not a composite number that can be broken down into primes), how do we talk about its prime factorization? This is where the concept of the "empty product" comes into play.

Why 1 is NOT Composite?

A composite number must be greater than 1.

A composite number must have more than two positive factors. The number 1 only has one.

Therefore, 1 is in a special category of its own. It is neither prime nor composite. It is often referred to as a "unit" in more advanced mathematics, especially in number theory and abstract algebra.