Factors of 7776
Factors of 7776 are the list of integers that we can split evenly into 7776. There are total 36 factors of 7776, of which 2, 3 are its prime factors. The Prime Factorization of 7776 is 2^{5} × 3^{5}.
 All Factors of 7776: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 864, 972, 1296, 1944, 2592, 3888 and 7776
 Prime Factors of 7776: 2, 3
 Prime Factorization of 7776: 2^{5} × 3^{5}
 Sum of Factors of 7776: 22932
1.  What Are the Factors of 7776? 
2.  Factors of 7776 by Prime Factorization 
3.  Factors of 7776 in Pairs 
4.  FAQs on Factors of 7776 
What are Factors of 7776?
Factors of 7776 are pairs of those numbers whose products result in 7776. These factors are either prime numbers or composite numbers.
How to Find the Factors of 7776?
To find the factors of 7776, we will have to find the list of numbers that would divide 7776 without leaving any remainder.
 7776/36 = 216; therefore, 36 is a factor of 7776 and 216 is also a factor of 7776.
 7776/54 = 144; therefore, 54 is a factor of 7776 and 144 is also a factor of 7776.
☛ Also Check:
 Factors of 34  The factors of 34 are 1, 2, 17, 34
 Factors of 25  The factors of 25 are 1, 5, 25
 Factors of 84  The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
 Factors of 7  The factors of 7 are 1, 7
 Factors of 32  The factors of 32 are 1, 2, 4, 8, 16, 32
Factors of 7776 by Prime Factorization
 7776 ÷ 2 = 3888
 3888 ÷ 2 = 1944
 1944 ÷ 2 = 972
 972 ÷ 2 = 486
 486 ÷ 2 = 243
Further dividing 243 by 2 gives a nonzero remainder. So we stop the process and continue dividing the number 243 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 7776 can be written as 2^{5} × 3^{5} where 2, 3 are prime.
Factors of 7776 in Pairs
Pair factors of 7776 are the pairs of numbers that when multiplied give the product 7776. The factors of 7776 in pairs are:
 1 × 7776 = (1, 7776)
 2 × 3888 = (2, 3888)
 3 × 2592 = (3, 2592)
 4 × 1944 = (4, 1944)
 6 × 1296 = (6, 1296)
 8 × 972 = (8, 972)
 9 × 864 = (9, 864)
 12 × 648 = (12, 648)
 16 × 486 = (16, 486)
 18 × 432 = (18, 432)
 24 × 324 = (24, 324)
 27 × 288 = (27, 288)
 32 × 243 = (32, 243)
 36 × 216 = (36, 216)
 48 × 162 = (48, 162)
 54 × 144 = (54, 144)
 72 × 108 = (72, 108)
 81 × 96 = (81, 96)
Negative pair factors of 7776 are:
 1 × 7776 = (1, 7776)
 2 × 3888 = (2, 3888)
 3 × 2592 = (3, 2592)
 4 × 1944 = (4, 1944)
 6 × 1296 = (6, 1296)
 8 × 972 = (8, 972)
 9 × 864 = (9, 864)
 12 × 648 = (12, 648)
 16 × 486 = (16, 486)
 18 × 432 = (18, 432)
 24 × 324 = (24, 324)
 27 × 288 = (27, 288)
 32 × 243 = (32, 243)
 36 × 216 = (36, 216)
 48 × 162 = (48, 162)
 54 × 144 = (54, 144)
 72 × 108 = (72, 108)
 81 × 96 = (81, 96)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 7776 Solved Examples

Example 1: How many factors are there for 7776?
Solution:
The factors of 7776 are too many, therefore if we can find the prime factorization of 7776, 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 7776 = 2^{5} × 3^{5}
Therefore, the total number of factors are (5 + 1) × (5 + 1) = 6 × 6 = 36 
Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 7776 and 6249.
Solution:
The factors of 7776 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 864, 972, 1296, 1944, 2592, 3888, 7776 and factors of 6249 are 1, 3, 2083, 6249.
Therefore, the Least Common Multiple (LCM) of 7776 and 6249 is 16197408 and Highest Common Factor (HCF) of 7776 and 6249 is 3. 
Example 3: Find if 3, 18, 72, 108, 243, 324, 1944 and 6941 are factors of 7776.
Solution:
When we divide 7776 by 6941 it leaves a remainder. Therefore, the number 6941 is not a factor of 7776. All numbers except 6941 are factors of 7776.

Example 4: Find the product of all the prime factors of 7776.
Solution:
Since, the prime factors of 7776 are 2, 3. Therefore, the product of prime factors = 2 × 3 = 6.
FAQs on Factors of 7776
What are the Factors of 7776?
The factors of 7776 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 864, 972, 1296, 1944, 2592, 3888, 7776 and its negative factors are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 864, 972, 1296, 1944, 2592, 3888, 7776.
What is the Sum of the Factors of 7776?
Sum of all factors of 7776 = (2^{5 + 1}  1)/(2  1) × (3^{5 + 1}  1)/(3  1) = 22932
What are Prime Factors of 7776?
The prime factors of 7776 are 2, 3.
What is the Greatest Common Factor of 7776 and 6157?
The factors of 7776 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 864, 972, 1296, 1944, 2592, 3888, 7776 and the factors of 6157 are 1, 47, 131, 6157. 7776 and 6157 have only one common factor which is 1. This implies that 7776 and 6157 are coprime.
Hence, the Greatest Common Factor (GCF) of 7776 and 6157 is 1.
What are the Common Factors of 7776 and 4725?
Since, the factors of 7776 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 864, 972, 1296, 1944, 2592, 3888, 7776 and the factors of 4725 are 1, 3, 5, 7, 9, 15, 21, 25, 27, 35, 45, 63, 75, 105, 135, 175, 189, 225, 315, 525, 675, 945, 1575, 4725.
Hence, [1, 3, 9, 27] are the common factors of 7776 and 4725.
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