Prime Factors of 407

Steps to find Prime Factors of 407 by Division Method

To find the primefactors of 407 using the division method, follow these steps:

• Step 1. Start dividing 407 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 407, which is 11. Divide 407 by 11 to obtain the quotient (37).
  407 ÷ 11 = 37
• Step 3. Repeat step 1 with the obtained quotient (37).
  37 ÷ 37 = 1

So, the prime factorization of 407 is, 407 = 11 x 37.

Steps to find Prime Factors of 407 by Factor Tree Method

We can follow the same procedure using the factor tree of 407 as shown below:

So, the prime factorization of 407 is, 407 = 11 x 37.

How do you define Prime Factors of a number?

Prime numbers, in mathematics are all those natural numbers greater than 1 that have exactly 2 factors which are 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 407 are 11 x 37.

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 407 but not a prime factor of 407.

Frequently Asked Questions

• Which is the smallest prime factor of 407?

  Smallest prime factor of 407 is 11.

• What are the factors of 407?

  Factors of 407 are 1 , 11 , 37 , 407.

• What is prime factorization of 407 in exponential form?

  Prime factorization of 407 in exponential form is 11 x 37.

• Is 407 a prime number or a composite number?

  407 is a composite number.

• Is 407 a prime number?

  false, 407 is not a prime number.

• What is the sum of all prime factors of 407?

  Prime factors of 407 are 11 x 37. Therefore, their sum is 48.

• What is the product of all prime factors of 407?

  Prime factors of 407 are 11 x 37. Therefore, their product is 407.

• What numbers are the prime factors of 407?

  Prime factors of 407 are 11 , 37.

• What is the sum of all odd prime factors of 407?

  Prime factors of 407 are 11 , 37, out of which 11 , 37 are odd numbers. So, the sum of odd prime factors of 407 is 11 + 37 = 48.