Factors of 728 in pair are (1, 728) , (2, 364) , (4, 182) , (7, 104) , (8, 91) , (13, 56) , (14, 52) and (26, 28)

How to find factors of a number in pair

Steps to find factors of 728 in pair

Example: Find factors of 728 in pair

Factor Pair Pair Factorization
1 and 728 1 x 728 = 728
2 and 364 2 x 364 = 728
4 and 182 4 x 182 = 728
7 and 104 7 x 104 = 728
8 and 91 8 x 91 = 728
13 and 56 13 x 56 = 728
14 and 52 14 x 52 = 728
26 and 28 26 x 28 = 728

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 728. They are called negative pair factors.

Hence, the negative pairs of 728 would be ( -1 , -728 ) .

What does factor pairs in mathematics mean?

In mathematics, factor pair of a number are all those possible combination which when multiplied together give the original number in return. Every natural number is a product of atleast one factor pair. Eg- Factors of 728 are 1 , 2 , 4 , 7 , 8 , 13 , 14 , 26 , 28 , 52 , 56 , 91 , 104 , 182 , 364 , 728. So, factors of 728 in pair are (1,728), (2,364), (4,182), (7,104), (8,91), (13,56), (14,52), (26,28).

What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

Properties of Factors

  • Each number is a factor of itself. Eg. 728 is a factor of itself.
  • 1 is a factor of every number. Eg. 1 is a factor of 728.
  • Every number is a factor of zero (0), since 728 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, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728 are exact divisors of 728.
  • Factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728. Each factor divides 728 without leaving a remainder.
  • Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728 are all less than or equal to 728.

Steps to find Factors of 728

  • Step 1. Find all the numbers that would divide 728 without leaving any remainder. Starting with the number 1 upto 364 (half of 728). The number 1 and the number itself are always factors of the given number.
    728 ÷ 1 : Remainder = 0
    728 ÷ 2 : Remainder = 0
    728 ÷ 4 : Remainder = 0
    728 ÷ 7 : Remainder = 0
    728 ÷ 8 : Remainder = 0
    728 ÷ 13 : Remainder = 0
    728 ÷ 14 : Remainder = 0
    728 ÷ 26 : Remainder = 0
    728 ÷ 28 : Remainder = 0
    728 ÷ 52 : Remainder = 0
    728 ÷ 56 : Remainder = 0
    728 ÷ 91 : Remainder = 0
    728 ÷ 104 : Remainder = 0
    728 ÷ 182 : Remainder = 0
    728 ÷ 364 : Remainder = 0
    728 ÷ 728 : Remainder = 0

Hence, Factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, and 728

Frequently Asked Questions

  • Is 728 a composite number?

    Yes 728 is a composite number.

  • Is 728 a prime number?

    No 728 is not a prime number.

  • Is 728 a perfect square?

    No 728 is not a perfect square.

  • Write five multiples of 728.

    Five multiples of 728 are 1456, 2184, 2912, 3640, 4368.

  • Write all odd factors of 728?

    The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728.
    Odd factors of 728 are 1 , 7 , 13 , 91.

Examples of Factors

Ariel has been asked to write all factor pairs of 728 but she is finding it difficult. Can you help her find out?

Factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728. So, factors of 728 in pair are (1,728), (2,364), (4,182), (7,104), (8,91), (13,56), (14,52), (26,28).

Sammy wants to write all the negative factors of 728 in pair, but don't know how to start. Help Sammy in writing all the factor pairs.

Negative factors of 728 are -1, -2, -4, -7, -8, -13, -14, -26, -28, -52, -56, -91, -104, -182, -364, -728. Hence, factors of 728 in pair are (-1,-728), (-2,-364), (-4,-182), (-7,-104), (-8,-91), (-13,-56), (-14,-52), (-26,-28).

Help Deep in writing the positive factors of 728 in pair and negative factor of 728 in pair.

Factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728. Positive factors of 728 in pair are (1,728), (2,364), (4,182), (7,104), (8,91), (13,56), (14,52), (26,28). Negative factors of 728 in pair are (-1,-728), (-2,-364), (-4,-182), (-7,-104), (-8,-91), (-13,-56), (-14,-52), (-26,-28).

Find the product of all factors of 728.

Factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728. So the product of all factors of 728 would be 1 x 2 x 4 x 7 x 8 x 13 x 14 x 26 x 28 x 52 x 56 x 91 x 104 x 182 x 364 x 728 = 7.889528230345372e+22.

Find the product of all prime factors of 728.

Factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728. Prime factors are 2, 2, 2, 7, 13. So, the product of all prime factors of 728 would be 2 x 2 x 2 x 7 x 13 = 728.

Can you help Sammy list the factors of 728 and also find the factor pairs?

Factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728.
Factors of 728 in pair are (1,728), (2,364), (4,182), (7,104), (8,91), (13,56), (14,52), (26,28).

Sammy has 728 blocks and he wants to arrange them in all possible ways to form a rectangle but he doesn't know the technique for doing that, help Sammy in arrangements.

To arrange 728 blocks in all possible ways to form a rectangle, we need to calculate factors of 728 in pair. Therefore, factors of 728 in pair are (1,728), (2,364), (4,182), (7,104), (8,91), (13,56), (14,52), (26,28)