Factors of 2592
Factors of 2592 are numbers that, when multiplied in pairs give the product as 2592. There are overall 30 factors of 2592 among which 2592 is the biggest factor and its prime factors are 2, 3. The Prime Factorization of 2592 is 25 × 34.
- All Factors of 2592: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 288, 324, 432, 648, 864, 1296 and 2592
- Prime Factors of 2592: 2, 3
- Prime Factorization of 2592: 25 × 34
- Sum of Factors of 2592: 7623
1. | What Are the Factors of 2592? |
2. | Factors of 2592 by Prime Factorization |
3. | Factors of 2592 in Pairs |
4. | FAQs on Factors of 2592 |
What are Factors of 2592?
Factors of 2592 are pairs of those numbers whose products result in 2592. These factors are either prime numbers or composite numbers.
How to Find the Factors of 2592?
To find the factors of 2592, we will have to find the list of numbers that would divide 2592 without leaving any remainder.
- 2592/1 = 2592; therefore, 1 is a factor of 2592.
- 2592/12 = 216; therefore, 12 is a factor of 2592.
☛ Also Check:
- Factors of 57 - The factors of 57 are 1, 3, 19, 57
- Factors of 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
- Factors of 52 - The factors of 52 are 1, 2, 4, 13, 26, 52
- Factors of 70 - The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
- Factors of 26 - The factors of 26 are 1, 2, 13, 26
Factors of 2592 by Prime Factorization
- 2592 ÷ 2 = 1296
- 1296 ÷ 2 = 648
- 648 ÷ 2 = 324
- 324 ÷ 2 = 162
- 162 ÷ 2 = 81
Further dividing 81 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 81 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 2592 can be written as 25 × 34 where 2, 3 are prime.
Factors of 2592 in Pairs
Pair factors of 2592 are the pairs of numbers that when multiplied give the product 2592. The factors of 2592 in pairs are:
- 1 × 2592 = (1, 2592)
- 2 × 1296 = (2, 1296)
- 3 × 864 = (3, 864)
- 4 × 648 = (4, 648)
- 6 × 432 = (6, 432)
- 8 × 324 = (8, 324)
- 9 × 288 = (9, 288)
- 12 × 216 = (12, 216)
- 16 × 162 = (16, 162)
- 18 × 144 = (18, 144)
- 24 × 108 = (24, 108)
- 27 × 96 = (27, 96)
- 32 × 81 = (32, 81)
- 36 × 72 = (36, 72)
- 48 × 54 = (48, 54)
Negative pair factors of 2592 are:
- -1 × -2592 = (-1, -2592)
- -2 × -1296 = (-2, -1296)
- -3 × -864 = (-3, -864)
- -4 × -648 = (-4, -648)
- -6 × -432 = (-6, -432)
- -8 × -324 = (-8, -324)
- -9 × -288 = (-9, -288)
- -12 × -216 = (-12, -216)
- -16 × -162 = (-16, -162)
- -18 × -144 = (-18, -144)
- -24 × -108 = (-24, -108)
- -27 × -96 = (-27, -96)
- -32 × -81 = (-32, -81)
- -36 × -72 = (-36, -72)
- -48 × -54 = (-48, -54)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 2592 Solved Examples
-
Example 1: How many factors are there for 2592?
Solution:
The factors of 2592 are too many, therefore if we can find the prime factorization of 2592, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is ax × by × cz 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 2592 = 25 × 34
Therefore, the total number of factors are (5 + 1) × (4 + 1) = 6 × 5 = 30 -
Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 2592 and 438.
Solution:
The factors of 2592 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 288, 324, 432, 648, 864, 1296, 2592 and factors of 438 are 1, 2, 3, 6, 73, 146, 219, 438.
Therefore, the Least Common Multiple (LCM) of 2592 and 438 is 189216 and Highest Common Factor (HCF) of 2592 and 438 is 6. -
Example 3: Find if 9, 27, 32, 48, 144, 162, 288 and 1741 are factors of 2592.
Solution:
When we divide 2592 by 1741 it leaves a remainder. Therefore, the number 1741 is not a factor of 2592. All numbers except 1741 are factors of 2592.
-
Example 4: Find the product of all the prime factors of 2592.
Solution:
Since, the prime factors of 2592 are 2, 3. Therefore, the product of prime factors = 2 × 3 = 6.
FAQs on Factors of 2592
What are the Factors of 2592?
The factors of 2592 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 288, 324, 432, 648, 864, 1296, 2592 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, -288, -324, -432, -648, -864, -1296, -2592.
What is the Sum of the Factors of 2592?
Sum of all factors of 2592 = (25 + 1 - 1)/(2 - 1) × (34 + 1 - 1)/(3 - 1) = 7623
What are Prime Factors of 2592?
The prime factors of 2592 are 2, 3.
What is the Greatest Common Factor of 2592 and 545?
The factors of 2592 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 288, 324, 432, 648, 864, 1296, 2592 and the factors of 545 are 1, 5, 109, 545. 2592 and 545 have only one common factor which is 1. This implies that 2592 and 545 are co-prime.
Hence, the Greatest Common Factor (GCF) of 2592 and 545 is 1.
How Many Factors of 2592 are also Factors of 1458?
Since, the factors of 2592 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 288, 324, 432, 648, 864, 1296, 2592 and the factors of 1458 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486, 729, 1458.
Hence, [1, 2, 3, 6, 9, 18, 27, 54, 81, 162] are the common factors of 2592 and 1458.
visual curriculum