# Prime Factors of 123

Prime Factors of 123 are 3 and 41

#### How to find prime factors of a number

 1.   Prime Factorization of 123 by Division Method 2.   Prime Factorization of 123 by Factor Tree Method 3.   Definition of Prime Factors 4.   Frequently Asked Questions

#### Steps to find Prime Factors of 123 by Division Method

To find the primefactors of 123 using the division method, follow these steps:

• Step 1. Start dividing 123 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 123, which is 3. Divide 123 by 3 to obtain the quotient (41).
123 ÷ 3 = 41
• Step 3. Repeat step 1 with the obtained quotient (41).
41 ÷ 41 = 1

So, the prime factorization of 123 is, 123 = 3 x 41.

#### Steps to find Prime Factors of 123 by Factor Tree Method

We can follow the same procedure using the factor tree of 123 as shown below:

So, the prime factorization of 123 is, 123 = 3 x 41.

#### What does Prime factor in mathematics mean?

Prime numbers, in mathematics are all those whole numbers greater than 1 having exactly two divisors that is 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 123 are 3 x 41.

#### Properties of Prime Factors

• For any given number there is one and only one set of unique prime factors.
• 2 is the only even prime number. So, any given number can have only one even prime factor and that is 2.
• Two prime factors of a given number 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 123 but not a prime factor of 123.

• Which is the smallest prime factor of 123?

Smallest prime factor of 123 is 3.

• Is 123 a perfect square?

No 123 is not a perfect square.

• What is the prime factorization of 123?

Prime factorization of 123 is 3 x 41.

• What is prime factorization of 123 in exponential form?

Prime factorization of 123 in exponential form is 3 x 41.

• Is 123 a prime number?

false, 123 is not a prime number.

• Which is the largest prime factors of 123?

The largest prime factor of 123 is 41.

• What is the product of all prime factors of 123?

Prime factors of 123 are 3 x 41. Therefore, their product is 123.

• What is the sum of all odd prime factors of 123?

Prime factors of 123 are 3 , 41, out of which 3 , 41 are odd numbers. So, the sum of odd prime factors of 123 is 3 + 41 = 44.

• What is the product of all odd prime factors of 123?

Prime factors of 123 are 3 , 41, out of which 3 , 41 are odd numbers. So, the product of odd prime factors of 123 is 3 x 41 = 123.