Factors of 37 | Prime Factorization of 37 - Explained Simply
Today we are going to present here Factor Tree of 37. The factor is the number that divides the original number. The Factors of 37 are 1 and 37 itself.
What are the factors of 37?
To find the factors of 37, we look for all integers that divide 37 evenly, meaning without a remainder. We can systematically check integers starting from 1.
Factor Tree Method of 37: Explained Simply
To find the factors of 37, we look for integers that divide 37 without leaving a remainder. We can systematically check numbers starting from 1:
1. Check divisibility by 1: Every integer is divisible by 1. $$37 \div 1 = 37$$
So, 1 and 37 are factors.
2. Check divisibility by prime numbers: To find other potential factors, we can check prime numbers up to the square root of 37. The square root of 37 is approximately \(\sqrt{37} \approx 6.08\). So, we only need to check prime numbers less than or equal to 6, which are 2, 3, and 5.
Check divisibility by 2: 37 is an odd number, so it is not divisible by 2. (i.e., \(37 \div 2 = 18 \text{ with a remainder of } 1\)).
Check divisibility by 3: To check for divisibility by 3, sum the digits: \(3 + 7 = 10\). Since 10 is not divisible by 3, 37 is not divisible by 3. (i.e., \(37 \div 3 = 12 \text{ with a remainder of } 1\)).
Check divisibility by 5: Numbers divisible by 5 must end in 0 or 5. 37 does not end in 0 or 5, so it is not divisible by 5. (i.e., \(37 \div 5 = 7 \text{ with a remainder of } 2\)).
Since 37 is not divisible by any prime number between 1 and itself, it means 37 is a prime number. Prime numbers have exactly two distinct factors: 1 and the number itself.
Therefore, the only factors of 37 are 1 and 37.
Prime Factorization of 37
Now, let's apply this thinking to our target number, 37. We need to determine if 37 is a prime number or a composite number. We'll do this by attempting to divide it by small prime numbers, starting from 2.
Steps to check if 37 is prime
Check divisibility by 2:
Is 37 an even number? No, it ends in 7, which is odd.
Therefore, 37 is not divisible by 2.
Check divisibility by 3:
A number is divisible by 3 if the sum of its digits is divisible by 3.
Sum of digits of 37 = 3 + 7 = 10.
Is 10 divisible by 3? No.
Therefore, 37 is not divisible by 3.
Check divisibility by 5:
A number is divisible by 5 if it ends in a 0 or a 5.
37 ends in 7.
Therefore, 37 is not divisible by 5.
Check divisibility by 7:
Let's divide 37 by 7: 37 ÷ 7 = 5 with a remainder of 2 (since 7 × 5 = 35).
Therefore, 37 is not divisible by 7.
When to stop checking?
A helpful rule of thumb is that you only need to check prime numbers up to the square root of the number you're factoring.
The square root of 37 is approximately 6.08. The prime numbers less than or equal to 6.08 are 2, 3, and 5. Since we've already checked 2, 3, and 5 (and even 7, just to be thorough), and found that 37 is not divisible by any of them, we can confidently conclude: 37 is a Prime Number.
The Prime Factorization of a Prime Number. This brings us to a unique and very simple answer for our original question. By definition, a prime number has only two factors: 1 and itself. When performing prime factorization, we are looking for the prime numbers that multiply together to form our target number.
If the number itself is prime, then it is its own prime factor.
The prime factorization of 37 is 37.