Prime Factors of 748

Steps to find Prime Factors of 748 by Division Method

To find the primefactors of 748 using the division method, follow these steps:

• Step 1. Start dividing 748 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 748, which is 2. Divide 748 by 2 to obtain the quotient (374).
  748 ÷ 2 = 374
• Step 3. Repeat step 1 with the obtained quotient (374).
  374 ÷ 2 = 187
  187 ÷ 11 = 17
  17 ÷ 17 = 1

So, the prime factorization of 748 is, 748 = 2 x 2 x 11 x 17.

Steps to find Prime Factors of 748 by Factor Tree Method

We can follow the same procedure using the factor tree of 748 as shown below:

So, the prime factorization of 748 is, 748 = 2 x 2 x 11 x 17.

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 748 are 2 x 2 x 11 x 17.

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 748 but not a prime factor of 748.

Frequently Asked Questions

• Which is the smallest prime factor of 748?

  Smallest prime factor of 748 is 2.

• What is the prime factorization of 748?

  Prime factorization of 748 is 2 x 2 x 11 x 17.

• What are the factors of 748?

  Factors of 748 are 1 , 2 , 4 , 11 , 17 , 22 , 34 , 44 , 68 , 187 , 374 , 748.

• Is 748 a prime number or a composite number?

  748 is a composite number.

• Is 748 a prime number?

  false, 748 is not a prime number.

• Which is the largest prime factors of 748?

  The largest prime factor of 748 is 17.

• What is the sum of all prime factors of 748?

  Prime factors of 748 are 2 x 2 x 11 x 17. Therefore, their sum is 32.

• What numbers are the prime factors of 748?

  Prime factors of 748 are 2 , 2 , 11 , 17.

• What is the sum of all odd prime factors of 748?

  Prime factors of 748 are 2 , 2 , 11 , 17, out of which 11 , 17 are odd numbers. So, the sum of odd prime factors of 748 is 11 + 17 = 28.