Prime Factors of 414

Steps to find Prime Factors of 414 by Division Method

To find the primefactors of 414 using the division method, follow these steps:

• Step 1. Start dividing 414 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 414, which is 2. Divide 414 by 2 to obtain the quotient (207).
  414 ÷ 2 = 207
• Step 3. Repeat step 1 with the obtained quotient (207).
  207 ÷ 3 = 69
  69 ÷ 3 = 23
  23 ÷ 23 = 1

So, the prime factorization of 414 is, 414 = 2 x 3 x 3 x 23.

Steps to find Prime Factors of 414 by Factor Tree Method

We can follow the same procedure using the factor tree of 414 as shown below:

So, the prime factorization of 414 is, 414 = 2 x 3 x 3 x 23.

What does Prime factor of a number mean?

A prime number in mathematics is defined as any natural number greater than 1, that is not divisible by any number except 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 414 are 2 x 3 x 3 x 23.

Properties of Prime Factors

• Two prime factors of a given number are always coprime to each other.
• 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 414 but not a prime factor of 414.

Frequently Asked Questions

• Which is the smallest prime factor of 414?

  Smallest prime factor of 414 is 2.

• Is 414 a perfect square?

  No 414 is not a perfect square.

• What is the prime factorization of 414?

  Prime factorization of 414 is 2 x 3 x 3 x 23.

• What are the factors of 414?

  Factors of 414 are 1 , 2 , 3 , 6 , 9 , 18 , 23 , 46 , 69 , 138 , 207 , 414.

• What is the product of all prime factors of 414?

  Prime factors of 414 are 2 x 3 x 3 x 23. Therefore, their product is 414.

• What numbers are the prime factors of 414?

  Prime factors of 414 are 2 , 3 , 3 , 23.

• What is the sum of all odd prime factors of 414?

  Prime factors of 414 are 2 , 3 , 3 , 23, out of which 3 , 3 , 23 are odd numbers. So, the sum of odd prime factors of 414 is 3 + 3 + 23 = 29.

• Is there any even prime factor of 414?

  Yes there is a even prime factor of 414.

• What is the product of all odd prime factors of 414?

  Prime factors of 414 are 2 , 3 , 3 , 23, out of which 3 , 3 , 23 are odd numbers. So, the product of odd prime factors of 414 is 3 x 3 x 23 = 207.