Prime Factors of 678

Steps to find Prime Factors of 678 by Division Method

To find the primefactors of 678 using the division method, follow these steps:

• Step 1. Start dividing 678 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 678, which is 2. Divide 678 by 2 to obtain the quotient (339).
  678 ÷ 2 = 339
• Step 3. Repeat step 1 with the obtained quotient (339).
  339 ÷ 3 = 113
  113 ÷ 113 = 1

So, the prime factorization of 678 is, 678 = 2 x 3 x 113.

Steps to find Prime Factors of 678 by Factor Tree Method

We can follow the same procedure using the factor tree of 678 as shown below:

So, the prime factorization of 678 is, 678 = 2 x 3 x 113.

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 678 are 2 x 3 x 113.

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 678 but not a prime factor of 678.

Frequently Asked Questions

• Which is the smallest prime factor of 678?

  Smallest prime factor of 678 is 2.

• Is 678 a perfect square?

  No 678 is not a perfect square.

• What is the prime factorization of 678?

  Prime factorization of 678 is 2 x 3 x 113.

• What are the factors of 678?

  Factors of 678 are 1 , 2 , 3 , 6 , 113 , 226 , 339 , 678.

• What is the product of all prime factors of 678?

  Prime factors of 678 are 2 x 3 x 113. Therefore, their product is 678.

• What numbers are the prime factors of 678?

  Prime factors of 678 are 2 , 3 , 113.

• What is the sum of all odd prime factors of 678?

  Prime factors of 678 are 2 , 3 , 113, out of which 3 , 113 are odd numbers. So, the sum of odd prime factors of 678 is 3 + 113 = 116.

• Is there any even prime factor of 678?

  Yes there is a even prime factor of 678.

• What is the product of all odd prime factors of 678?

  Prime factors of 678 are 2 , 3 , 113, out of which 3 , 113 are odd numbers. So, the product of odd prime factors of 678 is 3 x 113 = 339.