Prime Factors of 684

Steps to find Prime Factors of 684 by Division Method

To find the primefactors of 684 using the division method, follow these steps:

• Step 1. Start dividing 684 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 684, which is 2. Divide 684 by 2 to obtain the quotient (342).
  684 ÷ 2 = 342
• Step 3. Repeat step 1 with the obtained quotient (342).
  342 ÷ 2 = 171
  171 ÷ 3 = 57
  57 ÷ 3 = 19
  19 ÷ 19 = 1

So, the prime factorization of 684 is, 684 = 2 x 2 x 3 x 3 x 19.

Steps to find Prime Factors of 684 by Factor Tree Method

We can follow the same procedure using the factor tree of 684 as shown below:

So, the prime factorization of 684 is, 684 = 2 x 2 x 3 x 3 x 19.

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 684 are 2 x 2 x 3 x 3 x 19.

Properties of Prime Factors

• For any given number there is one and only one set of unique prime factors.
• Any number can have only 1 even prime factor and that is number 2.
• Two prime factors are always coprime to each other.
• 1 is the factor of any given number, but 1 is neither a prime number nor a composite number. So, 1 is the factor of 684 but not a prime factor of 684.

Frequently Asked Questions

• Which is the smallest prime factor of 684?

  Smallest prime factor of 684 is 2.

• What is the prime factorization of 684?

  Prime factorization of 684 is 2 x 2 x 3 x 3 x 19.

• What are the factors of 684?

  Factors of 684 are 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 19 , 36 , 38 , 57 , 76 , 114 , 171 , 228 , 342 , 684.

• Is 684 a prime number or a composite number?

  684 is a composite number.

• Is 684 a prime number?

  false, 684 is not a prime number.

• Which is the largest prime factors of 684?

  The largest prime factor of 684 is 19.

• What is the sum of all prime factors of 684?

  Prime factors of 684 are 2 x 2 x 3 x 3 x 19. Therefore, their sum is 29.

• What numbers are the prime factors of 684?

  Prime factors of 684 are 2 , 2 , 3 , 3 , 19.

• What is the sum of all odd prime factors of 684?

  Prime factors of 684 are 2 , 2 , 3 , 3 , 19, out of which 3 , 3 , 19 are odd numbers. So, the sum of odd prime factors of 684 is 3 + 3 + 19 = 25.