Factors of 7 | Factor Tree of 7 - Explained Simply

Today we are going to present here Factor Tree of 7. The factor is the number that divides the original number. The factors of 7 are 1 and 7 itself.

What are the factors of 7?

We want to find all the whole numbers that can divide 7 without leaving any remainder.

Factor Tree Method of 7: Explained Simply

To find its factors, we'll systematically check whole numbers starting from 1 to see if they divide 7 without a remainder.

Start with 1:

Can 1 divide 7 evenly?

Yes, 7 ÷ 1 = 7.

This tells us that 1 and 7 are factors of 7. (Remember, 1 is always a factor, and a number is always a factor of itself).

Try the next whole number: 2

Can 2 divide 7 evenly?

No, 7 ÷ 2 = 3 with a remainder of 1.

So, 2 is not a factor of 7.

Try the next whole number: 3

Can 3 divide 7 evenly?

No, 7 ÷ 3 = 2 with a remainder of 1.

So, 3 is not a factor of 7.

Try the next whole numbers: 4, 5, 6

You'll find that none of these numbers divide 7 evenly (e.g., 7 ÷ 4 = 1 remainder 3; 7 ÷ 5 = 1 remainder 2; 7 ÷ 6 = 1 remainder 1).

We've already established that 7 is a factor of 7 (from Step 1, paired with 1). Once you reach a potential factor that is greater than the square root of the original number (in this case, √7 ≈ 2.64), or you reach the number itself, you've found all possible factor pairs.

Therefore, after our systematic check, we can definitively say:

The only factors of 7 are 1 and 7.

Properties of 7

7 is an odd number, meaning it is not divisible by 2.
7 is a happy number. (A happy number is one where, if you replace the number by the sum of the squares of its digits, and repeat the process, you eventually reach 1. 1² + 0² = 1.)
7 is a special number in the search for very large prime numbers. If 2^p - 1 is prime, then 'p' is a Mersenne prime exponent. For p=3, 2^3 - 1 = 7 (which is prime). For p=7, 2^7 - 1 = 127 (which is also prime!).
7 is considered a safe prime. {A prime number 'p' is a safe prime if (p-1)/2 is also a prime number. For 7: (7 - 1) / 2 = 6 / 2 = 3. Since 3 is a prime number, 7 is considered a safe prime.}
A twin prime is a pair of prime numbers that differ by 2. (5, 7) is a twin prime pair.
A cousin prime is a pair of prime numbers that differ by 4. (7, 11) is a cousin prime pair.

Prime Factorization of 7

Why 7 is Prime?

The number 7 perfectly fits this definition:

It is greater than 1.

Its only positive divisors are 1 and 7. You cannot divide 7 evenly by 2, 3, 4, 5, or 6.

Since 7 is a prime number itself, its prime factorization is wonderfully simple:

The prime factorization of 7 is simply 7.

This means that 7 cannot be broken down into a product of smaller prime numbers. It stands alone as a fundamental building block in the world of numbers, much like elements in chemistry.