Factors of 1728 are integers that can be divided evenly into 1728. There are 28 factors of 1728 of which 1728 itself is the biggest factor and its prime factors are 2, 3 The sum of all factors of 1728 is 5080.

• All Factors of 1728: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864 and 1728
• Prime Factors of 1728: 2, 3
• Prime Factorization of 1728: 2⁶ × 3³
• Sum of Factors of 1728: 5080

1.	What Are the Factors of 1728?
2.	Factors of 1728 by Prime Factorization
3.	Factors of 1728 in Pairs
4.	FAQs on Factors of 1728

Factors of 1728 are pairs of those numbers whose products result in 1728. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1728?

To find the factors of 1728, we will have to find the list of numbers that would divide 1728 without leaving any remainder.

• 1728/432 = 4; therefore, 432 is a factor of 1728 and 4 is also a factor of 1728.
• 1728/108 = 16; therefore, 108 is a factor of 1728 and 16 is also a factor of 1728.

Similarly we can find other factors. Hence, the factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728.

☛ Also Check:

• Factors of 26 - The factors of 26 are 1, 2, 13, 26
• Factors of 14 - The factors of 14 are 1, 2, 7, 14
• Factors of 7 - The factors of 7 are 1, 7
• Factors of 91 - The factors of 91 are 1, 7, 13, 91
• Factors of 80 - The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

The number 1728 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1728. The first step is to divide the number 1728 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

• 1728 ÷ 2 = 864
• 864 ÷ 2 = 432
• 432 ÷ 2 = 216
• 216 ÷ 2 = 108
• 108 ÷ 2 = 54
• 54 ÷ 2 = 27

Further dividing 27 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 27 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 1728 can be written as 2⁶ × 3³ where 2, 3 are prime.

Pair factors of 1728 are the pairs of numbers that when multiplied give the product 1728. The factors of 1728 in pairs are:

• 1 × 1728 = (1, 1728)
• 2 × 864 = (2, 864)
• 3 × 576 = (3, 576)
• 4 × 432 = (4, 432)
• 6 × 288 = (6, 288)
• 8 × 216 = (8, 216)
• 9 × 192 = (9, 192)
• 12 × 144 = (12, 144)
• 16 × 108 = (16, 108)
• 18 × 96 = (18, 96)
• 24 × 72 = (24, 72)
• 27 × 64 = (27, 64)
• 32 × 54 = (32, 54)
• 36 × 48 = (36, 48)

Negative pair factors of 1728 are:

• -1 × -1728 = (-1, -1728)
• -2 × -864 = (-2, -864)
• -3 × -576 = (-3, -576)
• -4 × -432 = (-4, -432)
• -6 × -288 = (-6, -288)
• -8 × -216 = (-8, -216)
• -9 × -192 = (-9, -192)
• -12 × -144 = (-12, -144)
• -16 × -108 = (-16, -108)
• -18 × -96 = (-18, -96)
• -24 × -72 = (-24, -72)
• -27 × -64 = (-27, -64)
• -32 × -54 = (-32, -54)
• -36 × -48 = (-36, -48)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.