Factors of 33 | Prime Factorization of 33 - Explained Simply

Today we are going to present here Factor Tree of 33. The factor is the number that divides the original number. The Factors of 33 are 1, 3, 11 and 33 itself.

What are the factors of 33?

To find the factors of 33, we look for all integers that divide 33 evenly, meaning without a remainder. We can systematically check integers starting from 1.

Factor Tree Method of 33: Explained Simply

Let's apply our understanding to find the factors of 33. We can use a systematic division method.

Method Division

To find all positive factors of 33, we'll try dividing 33 by whole numbers starting from 1, and see if the division is exact (no remainder). We only need to test numbers up to the square root of 33, which is approximately 5.7. This is because factors come in pairs; if we find a factor `x` where `x y = 33`, then `y` will be less than or equal to `x` if `x` is greater than or equal to the square root of 33, or vice-versa.

Start with 1:

$$33 \div 1 = 33$$

1 and 33 are factors of 33.

Try 2:

$$33 \div 2 = 16.5$$ (not an exact division)

2 is not a factor of 33. (This is expected, as 33 is an odd number).

Try 3:

$$33 \div 3 = 11$$

3 and 11 are factors of 33.

Try 4:

$$33 \div 4 = 8.25$$ (not exact)

4 is not a factor of 33.

Try 5:

$$33 \div 5 = 6.6$$ (not exact)

5 is not a factor of 33.

At this point, we've tested up to 5. Since the next number we'd test is 6, and 6 is greater than the square root of 33 (approx 5.7), we can stop. We've found all the unique pairs. The factors we found are 1, 3, 11, and 33.

Prime Factorization of 33

Now, let's apply these methods to our target number, 33.

Using the Division Method for 33:

Start with 33.

What is the smallest prime number that divides 33?

Is it divisible by 2?

No (33 is an odd number).

Is it divisible by 3?

Yes! (3 + 3 = 6, and 6 is divisible by 3).

Divide 33 by 3:

```

3 | 33

| 11

```

Now we have 11. Is 11 a prime number?

Yes, 11 is only divisible by 1 and 11.

Since 11 is prime, we stop.

The prime factors of 33 are 3 and 11.

Therefore, the prime factorization of 33 is 3 × 11.

Using the Factor Tree Method for 33:

Start with 33 at the top.

Find any two factors of 33. We know from our division method that 3 and 11 are factors.

```

/ \

3 11

```

Check if 3 is prime. Yes, it is. Circle it.

Check if 11 is prime. Yes, it is. Circle it.

```

/ \

③ ⑪

```

All the "leaves" of our tree are now circled prime numbers.

The prime factors of 33 are 3 and 11.

Therefore, the prime factorization of 33 is also 3 × 11.

Both methods lead to the same unique prime factorization, confirming the Fundamental Theorem of Arithmetic!