Prime Factors of 1764

Steps to find Prime Factors of 1764 by Division Method

To find the primefactors of 1764 using the division method, follow these steps:

• Step 1. Start dividing 1764 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 1764, which is 2. Divide 1764 by 2 to obtain the quotient (882).
  1764 ÷ 2 = 882
• Step 3. Repeat step 1 with the obtained quotient (882).
  882 ÷ 2 = 441
  441 ÷ 3 = 147
  147 ÷ 3 = 49
  49 ÷ 7 = 7
  7 ÷ 7 = 1

So, the prime factorization of 1764 is, 1764 = 2 x 2 x 3 x 3 x 7 x 7.

Steps to find Prime Factors of 1764 by Factor Tree Method

We can follow the same procedure using the factor tree of 1764 as shown below:

So, the prime factorization of 1764 is, 1764 = 2 x 2 x 3 x 3 x 7 x 7.

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 1764 are 2 x 2 x 3 x 3 x 7 x 7.

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 1764 but not a prime factor of 1764.

Frequently Asked Questions

• Which is the smallest prime factor of 1764?

  Smallest prime factor of 1764 is 2.

• What is the prime factorization of 1764?

  Prime factorization of 1764 is 2 x 2 x 3 x 3 x 7 x 7.

• What are the factors of 1764?

  Factors of 1764 are 1 , 2 , 3 , 4 , 6 , 7 , 9 , 12 , 14 , 18 , 21 , 28 , 36 , 42 , 49 , 63 , 84 , 98 , 126 , 147 , 196 , 252 , 294 , 441 , 588 , 882 , 1764.

• Is 1764 a prime number or a composite number?

  1764 is a composite number.

• Is 1764 a prime number?

  false, 1764 is not a prime number.

• Which is the largest prime factors of 1764?

  The largest prime factor of 1764 is 7.

• What is the sum of all prime factors of 1764?

  Prime factors of 1764 are 2 x 2 x 3 x 3 x 7 x 7. Therefore, their sum is 24.

• What numbers are the prime factors of 1764?

  Prime factors of 1764 are 2 , 2 , 3 , 3 , 7 , 7.

• What is the sum of all odd prime factors of 1764?

  Prime factors of 1764 are 2 , 2 , 3 , 3 , 7 , 7, out of which 3 , 3 , 7 , 7 are odd numbers. So, the sum of odd prime factors of 1764 is 3 + 3 + 7 + 7 = 20.