Factors of 38 | Prime Factorization of 38 - Explained Simply

Today we are going to present here Factor Tree of 38. The factor is the number that divides the original number. The Factors of 38 are 1, 2, 19 and 38 itself.

What are the factors of 38?

To find the factors of 38, we look for all integers that divide 38 evenly, meaning without a remainder. We can systematically check integers starting from 1.

Factor Tree Method of 38: Explained Simply

To find the factors of a number, we look for integers that divide the number evenly without leaving a remainder. We can systematically check numbers starting from 1 up to the square root of the given number.

The number in question is 38.

1. Start with 1: Every integer has 1 as a factor.

    $$1 \times 38 = 38$$

    So, 1 and 38 are factors.

2. Check for 2: Since 38 is an even number, it is divisible by 2.

    $$38 \div 2 = 19$$

    So, 2 and 19 are factors.

3. Check for 3: To check for divisibility by 3, sum the digits: 

   $$3 + 8 = 11$$.

    Since 11 is not divisible by 3, 38 is not divisible by 3.

4. Check for 4: Divide 38 by 4.

    $$38 \div 4 = 9 \text{ with a remainder of } 2$$

    So, 4 is not a factor.

5. Check for 5: A number is divisible by 5 if its last digit is 0 or 5. The last digit of 38 is 8, so it is not divisible by 5.

6. Check for numbers up to the square root of 38. The square root of 38 is approximately 

    $$\sqrt{38} \approx 6.16$$

    We need to check integers up to 6.

    We have already checked 1, 2, 3, 4, 5. The next integer to check is 6.

    A number is divisible by 6 if it is divisible by both 2 and 3. We found that 38 is divisible by 2 but not by 3, so it is not divisible by 6.

At this point, we have found factors 1, 2, 19, and 38. Since 19 is a prime number and we have checked all integers up to approximately 

\(\sqrt{38}\), we have found all unique factors. The factors appear in pairs: (1, 38) and (2, 19).

Arranging them in ascending order, the factors of 38 are 1, 2, 19, and 38.

Prime Factorization of 38

To find the prime factorization of 38, we systematically divide the number by the smallest prime numbers until the quotient is also a prime number. 

Step 1: Divide by the smallest prime number (2).

The number 38 is even, so it is divisible by 2. 38 ÷ 2 = 19

Step 2: Determine if the quotient (19) is prime.

We check if 19 is divisible by any prime numbers smaller than or equal to its square root (which is approximately 4.35). The primes to check are 2 and 3.

 19 is not divisible by 2 (it is odd).

The sum of the digits of 19 is $1+9=10$, which is not divisible by 3, so 19 is not divisible by 3. Since 19 is not divisible by any prime number less than or equal to its square root, 19 is a prime number.

Step 3: Write the factorization.

The prime factorization of 38 is the product of the divisors and the final prime quotient. 38 = 2 × 19

Factor Tree of 38

A factor tree is used to find the prime factorization of a composite number. We break the number down into pairs of factors until all resulting factors are prime numbers.

The number we are factoring is 38.

Step 1: Start the factor tree with 38 at the top.

Step 2: Find two factors whose product is 38. Since 38 is an even number, we can start by dividing it by the smallest prime number, 2.$$\frac{38}{2} = 19$$So, 38 can be written as the product of 2 and 19:$$38 = 2 \times 19$$

Step 3: Check if the resulting factors (2 and 19) are prime numbers.

The number 2 is a prime number.

The number 19 is also a prime number (it is only divisible by 1 and itself).

Step 4: Since both branches of the tree end in prime numbers, the factor tree is complete.

The resulting prime factors are 2 and 19.

The factor tree structure is visually represented as:$$38$$$$/ \quad \setminus$$$$2 \quad 19$$Thus, the prime factorization of 38 is \(2 \times 19\).