# Prime Factors of 1408

Prime Factors of 1408 are 2, 2, 2, 2, 2, 2, 2, and 11

#### How to find prime factors of a number

 1.   Prime Factorization of 1408 by Division Method 2.   Prime Factorization of 1408 by Factor Tree Method 3.   Definition of Prime Factors 4.   Frequently Asked Questions

#### Steps to find Prime Factors of 1408 by Division Method

To find the primefactors of 1408 using the division method, follow these steps:

• Step 1. Start dividing 1408 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 1408, which is 2. Divide 1408 by 2 to obtain the quotient (704).
1408 ÷ 2 = 704
• Step 3. Repeat step 1 with the obtained quotient (704).
704 ÷ 2 = 352
352 ÷ 2 = 176
176 ÷ 2 = 88
88 ÷ 2 = 44
44 ÷ 2 = 22
22 ÷ 2 = 11
11 ÷ 11 = 1

So, the prime factorization of 1408 is, 1408 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11.

#### Steps to find Prime Factors of 1408 by Factor Tree Method

We can follow the same procedure using the factor tree of 1408 as shown below:

So, the prime factorization of 1408 is, 1408 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11.

#### 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 1408 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11.

#### 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 1408 but not a prime factor of 1408.

• Which is the smallest prime factor of 1408?

Smallest prime factor of 1408 is 2.

• Is 1408 a perfect square?

No 1408 is not a perfect square.

• What is the prime factorization of 1408?

Prime factorization of 1408 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11.

• What is prime factorization of 1408 in exponential form?

Prime factorization of 1408 in exponential form is 27 x 11.

• Is 1408 a prime number or a composite number?

1408 is a composite number.

• Which is the largest prime factors of 1408?

The largest prime factor of 1408 is 11.

• What is the product of all prime factors of 1408?

Prime factors of 1408 are 2 x 2 x 2 x 2 x 2 x 2 x 2 x 11. Therefore, their product is 1408.

• What numbers are the prime factors of 1408?

Prime factors of 1408 are 2 , 2 , 2 , 2 , 2 , 2 , 2 , 11.

• Is there any even prime factor of 1408?

Yes there is a even prime factor of 1408.