Factors of 768
Factors of 768 are the list of integers that can be evenly divided into 768. There are overall 18 factors of 768, of which 2, 3 are its prime factors. The Prime Factorization of 768 is 2^{8} × 3^{1}.
 All Factors of 768: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384 and 768
 Prime Factors of 768: 2, 3
 Prime Factorization of 768: 2^{8} × 3^{1}
 Sum of Factors of 768: 2044
1.  What Are the Factors of 768? 
2.  Factors of 768 by Prime Factorization 
3.  Factors of 768 in Pairs 
4.  FAQs on Factors of 768 
What are Factors of 768?
Factors of 768 are pairs of those numbers whose products result in 768. These factors are either prime numbers or composite numbers.
How to Find the Factors of 768?
To find the factors of 768, we will have to find the list of numbers that would divide 768 without leaving any remainder.
 768/192 = 4; therefore, 192 is a factor of 768 and 4 is also a factor of 768.
 768/384 = 2; therefore, 384 is a factor of 768 and 2 is also a factor of 768.
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Factors of 768 by Prime Factorization
 768 ÷ 2 = 384
 384 ÷ 2 = 192
 192 ÷ 2 = 96
 96 ÷ 2 = 48
 48 ÷ 2 = 24
 24 ÷ 2 = 12
 12 ÷ 2 = 6
 6 ÷ 2 = 3
Further dividing 3 by 2 gives a nonzero remainder. So we stop the process and continue dividing the number 3 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.
So, the prime factorization of 768 can be written as 2^{8} × 3^{1} where 2, 3 are prime.
Factors of 768 in Pairs
Pair factors of 768 are the pairs of numbers that when multiplied give the product 768. The factors of 768 in pairs are:
 1 × 768 = (1, 768)
 2 × 384 = (2, 384)
 3 × 256 = (3, 256)
 4 × 192 = (4, 192)
 6 × 128 = (6, 128)
 8 × 96 = (8, 96)
 12 × 64 = (12, 64)
 16 × 48 = (16, 48)
 24 × 32 = (24, 32)
Negative pair factors of 768 are:
 1 × 768 = (1, 768)
 2 × 384 = (2, 384)
 3 × 256 = (3, 256)
 4 × 192 = (4, 192)
 6 × 128 = (6, 128)
 8 × 96 = (8, 96)
 12 × 64 = (12, 64)
 16 × 48 = (16, 48)
 24 × 32 = (24, 32)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 768 Solved Examples

Example 1: How many factors are there for 768?
Solution:
The factors of 768 are too many, therefore if we can find the prime factorization of 768, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^{x} × b^{y} × c^{z} where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).
Prime Factorization of 768 = 2^{8} × 3^{1}
Therefore, the total number of factors are (8 + 1) × (1 + 1) = 9 × 2 = 18 
Example 2: Find the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of 768 and 577.
Solution:
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768 and factors of 577 are 1, 577.
Therefore, the Lowest Common Multiple (LCM) of 768 and 577 is 443136 and Highest Common Factor (HCF) of 768 and 577 is 1. 
Example 3: Find if 1, 6, 12, 16, 24, 32, 256 and 482 are factors of 768.
Solution:
When we divide 768 by 482 it leaves a remainder. Therefore, the number 482 is not a factor of 768. All numbers except 482 are factors of 768.

Example 4: Find the product of all the prime factors of 768.
Solution:
Since, the prime factors of 768 are 2, 3. Therefore, the product of prime factors = 2 × 3 = 6.
FAQs on Factors of 768
What are the Factors of 768?
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768 and its negative factors are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768.
What is the Sum of all the Factors of 768?
Sum of all factors of 768 = (2^{8 + 1}  1)/(2  1) × (3^{1 + 1}  1)/(3  1) = 2044
What are the Pair Factors of 768?
The pair factors of 768 are (1, 768), (2, 384), (3, 256), (4, 192), (6, 128), (8, 96), (12, 64), (16, 48), (24, 32).
What is the Greatest Common Factor of 768 and 350?
The factors of 768 and 350 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768 and 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350 respectively.
Common factors of 768 and 350 are [1, 2].
Hence, the Greatest Common Factor of 768 and 350 is 2.
How Many Factors of 295 are also common to the Factors of 768?
Since, the factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768 and factors of 295 are 1, 5, 59, 295. Hence, 768 and 295 have only one common factor which is 1. Therefore, 768 and 295 are coprime.
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