Prime Factors of 105

Steps to find Prime Factors of 105 by Division Method

To find the primefactors of 105 using the division method, follow these steps:

• Step 1. Start dividing 105 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 105, which is 3. Divide 105 by 3 to obtain the quotient (35).
  105 ÷ 3 = 35
• Step 3. Repeat step 1 with the obtained quotient (35).
  35 ÷ 5 = 7
  7 ÷ 7 = 1

So, the prime factorization of 105 is, 105 = 3 x 5 x 7.

Steps to find Prime Factors of 105 by Factor Tree Method

We can follow the same procedure using the factor tree of 105 as shown below:

So, the prime factorization of 105 is, 105 = 3 x 5 x 7.

Definition of Prime Factors?

In mathematics, prime numbers are defined as all those whole numbers greater than 1 that have only two factors, i.e. 1 and the number itself. When we express any number as the product of these prime numbers than these prime numbers become prime factors of that number. Eg- Prime Factors of 105 are 3 x 5 x 7.

Properties of Prime Factors

• Prime factors are the set of factors that are unique to the number given.
• 2 is the only even prime factor any number can have.
• Two prime factors are always coprime to each other.
• 1 is neither a prime number nor a composite number and also 1 is the factor of every given number. So, 1 is the factor of 105 but not a prime factor of 105.

Frequently Asked Questions

• Which is the smallest prime factor of 105?

  Smallest prime factor of 105 is 3.

• What is the prime factorization of 105?

  Prime factorization of 105 is 3 x 5 x 7.

• What is prime factorization of 105 in exponential form?

  Prime factorization of 105 in exponential form is 3 x 5 x 7.

• Is 105 a prime number or a composite number?

  105 is a composite number.

• Is 105 a prime number?

  false, 105 is not a prime number.

• How to find prime factorization of 105 easily?

  To find prime factorization of 105 easily you can refer to the steps given on this page step by step.

• Which is the largest prime factors of 105?

  The largest prime factor of 105 is 7.

• What is the product of all prime factors of 105?

  Prime factors of 105 are 3 x 5 x 7. Therefore, their product is 105.

• What is the sum of all odd prime factors of 105?

  Prime factors of 105 are 3 , 5 , 7, out of which 3 , 5 , 7 are odd numbers. So, the sum of odd prime factors of 105 is 3 + 5 + 7 = 15.