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, and 7776

How to find factors of a number

1. Steps to find factors of 7776 using Division Method

Example: Find factors of 7776

  • Divide 7776 by 1: 7776 ÷ 1 : Remainder = 0
  • Divide 7776 by 2: 7776 ÷ 2 : Remainder = 0
  • Divide 7776 by 3: 7776 ÷ 3 : Remainder = 0
  • Divide 7776 by 4: 7776 ÷ 4 : Remainder = 0
  • Divide 7776 by 6: 7776 ÷ 6 : Remainder = 0
  • Divide 7776 by 8: 7776 ÷ 8 : Remainder = 0
  • Divide 7776 by 9: 7776 ÷ 9 : Remainder = 0
  • Divide 7776 by 12: 7776 ÷ 12 : Remainder = 0
  • Divide 7776 by 16: 7776 ÷ 16 : Remainder = 0
  • Divide 7776 by 18: 7776 ÷ 18 : Remainder = 0
  • Divide 7776 by 24: 7776 ÷ 24 : Remainder = 0
  • Divide 7776 by 27: 7776 ÷ 27 : Remainder = 0
  • Divide 7776 by 32: 7776 ÷ 32 : Remainder = 0
  • Divide 7776 by 36: 7776 ÷ 36 : Remainder = 0
  • Divide 7776 by 48: 7776 ÷ 48 : Remainder = 0
  • Divide 7776 by 54: 7776 ÷ 54 : Remainder = 0
  • Divide 7776 by 72: 7776 ÷ 72 : Remainder = 0
  • Divide 7776 by 81: 7776 ÷ 81 : Remainder = 0
  • Divide 7776 by 96: 7776 ÷ 96 : Remainder = 0
  • Divide 7776 by 108: 7776 ÷ 108 : Remainder = 0
  • Divide 7776 by 144: 7776 ÷ 144 : Remainder = 0
  • Divide 7776 by 162: 7776 ÷ 162 : Remainder = 0
  • Divide 7776 by 216: 7776 ÷ 216 : Remainder = 0
  • Divide 7776 by 243: 7776 ÷ 243 : Remainder = 0
  • Divide 7776 by 288: 7776 ÷ 288 : Remainder = 0
  • Divide 7776 by 324: 7776 ÷ 324 : Remainder = 0
  • Divide 7776 by 432: 7776 ÷ 432 : Remainder = 0
  • Divide 7776 by 486: 7776 ÷ 486 : Remainder = 0
  • Divide 7776 by 648: 7776 ÷ 648 : Remainder = 0
  • Divide 7776 by 864: 7776 ÷ 864 : Remainder = 0
  • Divide 7776 by 972: 7776 ÷ 972 : Remainder = 0
  • Divide 7776 by 1296: 7776 ÷ 1296 : Remainder = 0
  • Divide 7776 by 1944: 7776 ÷ 1944 : Remainder = 0
  • Divide 7776 by 2592: 7776 ÷ 2592 : Remainder = 0
  • Divide 7776 by 3888: 7776 ÷ 3888 : Remainder = 0
  • Divide 7776 by 7776: 7776 ÷ 7776 : Remainder = 0

Hence, 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, and 7776

2. Steps to find factors of 7776 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

Method 1: Division Method

To find the primefactors of 7776 using the division method, follow these steps:

  • Step 1. Start dividing 7776 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 7776, which is 2. Divide 7776 by 2 to obtain the quotient (3888).
    7776 ÷ 2 = 3888
  • Step 3. Repeat step 1 with the obtained quotient (3888).
    3888 ÷ 2 = 1944
    1944 ÷ 2 = 972
    972 ÷ 2 = 486
    486 ÷ 2 = 243
    243 ÷ 3 = 81
    81 ÷ 3 = 27
    27 ÷ 3 = 9
    9 ÷ 3 = 3
    3 ÷ 3 = 1

So, the prime factorization of 7776 is, 7776 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3.

Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 7776 as shown below:

So, the prime factorization of 7776 is, 7776 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3.

3. Find factors of 7776 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 7776 would be the two numbers which, when multiplied, give 7776 as the result.

The following table represents the calculation of factors of 7776 in pairs:

Factor Pair Pair Factorization
1 and 7776 1 x 7776 = 7776
2 and 3888 2 x 3888 = 7776
3 and 2592 3 x 2592 = 7776
4 and 1944 4 x 1944 = 7776
6 and 1296 6 x 1296 = 7776
8 and 972 8 x 972 = 7776
9 and 864 9 x 864 = 7776
12 and 648 12 x 648 = 7776
16 and 486 16 x 486 = 7776
18 and 432 18 x 432 = 7776
24 and 324 24 x 324 = 7776
27 and 288 27 x 288 = 7776
32 and 243 32 x 243 = 7776
36 and 216 36 x 216 = 7776
48 and 162 48 x 162 = 7776
54 and 144 54 x 144 = 7776
72 and 108 72 x 108 = 7776
81 and 96 81 x 96 = 7776

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 7776. They are called negative pair factors.

Hence, the negative pairs of 7776 would be ( -1 , -7776 ) , ( -2 , -3888 ) , ( -3 , -2592 ) , ( -4 , -1944 ) , ( -6 , -1296 ) , ( -8 , -972 ) , ( -9 , -864 ) , ( -12 , -648 ) , ( -16 , -486 ) , ( -18 , -432 ) , ( -24 , -324 ) , ( -27 , -288 ) , ( -32 , -243 ) , ( -36 , -216 ) , ( -48 , -162 ) , ( -54 , -144 ) , ( -72 , -108 ) and ( -81 , -96 ) .

How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

Properties of factors

  • Each number is a factor of itself. Eg. 7776 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 7776.
  • Every number is a factor of zero (0), since 7776 x 0 = 0.
  • Every number other than 1 has at least two factors, namely the number itself and 1.
  • Every factor of a number is an exact divisor of that number, example 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 are exact divisors of 7776.
  • 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. Each factor divides 7776 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 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 are all less than or equal to 7776.

Frequently Asked Questions

  • Which is the smallest prime factor of 7776?

    Smallest prime factor of 7776 is 2.

  • Is 7776 a perfect square?

    No 7776 is not a perfect square.

  • What are five multiples of 7776?

    First five multiples of 7776 are 15552, 23328, 31104, 38880, 46656.

  • What is prime factorization of 7776?

    Prime factorization of 7776 is 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3.

  • What are factors of 7776?

    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.

  • How do you find factors of a negative number? ( eg. -7776 )?

    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.

  • Is 7776 a whole number?

    Yes 7776 is a whole number.

  • Which is greatest factor of 7776?

    The greatest factor of 7776 is 3888.

  • What are the prime 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.
    Prime factors of 7776 are 2, 2, 2, 2, 2, 3, 3, 3, 3, 3.

Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 7776. Can you help her?

Prime factors of 7776 are 2, 2, 2, 2, 2, 3, 3, 3, 3, 3.
Hence, the product of prime factors of 6.

Can you help Rubel to find out the product of the even factors of 7776?

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.
Even factors of 7776 are 2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 54, 72, 96, 108, 144, 162, 216, 288, 324, 432, 486, 648, 864, 972, 1296, 1944, 2592, 3888, 7776.
Hence, product of even factors of 7776 is; 2 x 4 x 6 x 8 x 12 x 16 x 18 x 24 x 32 x 36 x 48 x 54 x 72 x 96 x 108 x 144 x 162 x 216 x 288 x 324 x 432 x 486 x 648 x 864 x 972 x 1296 x 1944 x 2592 x 3888 x 7776 = 7.52997811077866e+62.

Joy wants to calculate mean of all the factors of 7776. Help him in finding the mean of 7776.

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.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 7776 is 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 = 22932.
Hence, the mean of factors of 7776 is 22932 ÷ 36 = 637.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 7776? Help her in writing all the factors.

Positive 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.
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.

How many factors are there for 7776?

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.
So there are in total 36 factors.

Joey wants to write all the prime factors of 7776 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 7776 are 2, 2, 2, 2, 2, 3, 3, 3, 3, 3.
So in exponential form it can be written as 25 x 35.

Kevin has been asked to write 35 factor(s) of 7776. Can you predict the answer?

35 factor(s) 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.