Factors of 35 | Prime Factorization of 35 - Explained Simply

Today we are going to present here Factor Tree of 35. The factor is the number that divides the original number. The Factors of 35 are 1, 5, 7 and 35 itself.

What are the factors of 35?

To find the factors of 35, we look for all integers that divide 35 evenly, meaning without a remainder. We can systematically check integers starting from 1.

Factor Tree Method of 35: Explained Simply

Let's apply our methods to find all the factors of 35.

Using the Division/Factor Pair Method

Start with 1:

1 divides into 35 evenly: 35 ÷ 1 = 35.

Factor Pair 1: (1, 35)

So, 1 and 35 are factors.

Check 2:

Is 35 divisible by 2? No, because 35 is an odd number. (35 ÷ 2 = 17 with a remainder of 1).

So, 2 is not a factor.

Check 3:

To check for divisibility by 3, add the digits: 3 + 5 = 8. Is 8 divisible by 3? No.

So, 3 is not a factor.

Check 4:

Is 35 divisible by 4? No (4 x 8 = 32, 4 x 9 = 36).

So, 4 is not a factor.

Check 5:

Does 35 end in a 0 or a 5? Yes, it ends in 5.

35 ÷ 5 = 7.

Factor Pair 2: (5, 7)

So, 5 and 7 are factors.

Check 6:

Is 35 divisible by 6? No (6 x 5 = 30, 6 x 6 = 36).

So, 6 is not a factor.

Check 7:

We've already found 7 as part of the (5, 7) factor pair. Notice that we've now reached a number (7) that is greater than the square root of 35 (approximately 5.9). This means we've found all unique factor pairs. If we continue, we would just swap the order of the pairs we've already found (e.g., 7 x 5 = 35).

Consolidating the Factors:

From our factor pairs (1, 35) and (5, 7), we collect all the unique numbers:

The factors of 35 are: 1, 5, 7, and 35.

Prime Factorization of 35

Now, let's put these methods into practice to find the prime factorization of 35.

Is 35 Prime or Composite?

First, let's determine if 35 is prime or composite.

Is it greater than 1? Yes.

Does it have only factors 1 and 35? No. We know 5 divides 35 (5 × 7 = 35).

Therefore, 35 is a composite number.

A. Using the Division Method for 35:

Start with 35.

What's the smallest prime number that divides 35 evenly?

Is it divisible by 2? No, 35 is an odd number.

Is it divisible by 3? To check, add the digits: 3 + 5 = 8. 8 is not divisible by 3, so 35 is not.

Is it divisible by 5? Yes, 35 ends in a 5.

35 ÷ 5 = 7

Now we have the number 7. Is 7 a prime number? Yes, its only factors are 1 and 7.

We stop here because we've reached a prime number.

The prime factors are the numbers on the left (5) and the final prime number at the bottom (7).

Therefore, the prime factorization of 35 is 5 × 7.

Factor Tree Method for 35

Start with 35 at the top.

Think of any two numbers that multiply to give 35. We know 5 and 7 work.

Draw branches: 35

/ \

5 7

Check if 5 is prime. Yes. Circle it.

Check if 7 is prime. Yes. Circle it.

All the numbers at the end of the branches are now prime.

Therefore, the prime factorization of 35 is 5 × 7.

The Prime Factorization of 35

As you can see from both methods, the prime factorization of 35 is:

35 = 5 × 7

This means that 5 and 7 are the unique prime building blocks that multiply together to form the number 35.