Factors of 2448
Factors of 2448 are integers that can be divided evenly into 2448. There are 30 factors of 2448, of which the following are its prime factors 2, 3, 17. The sum of all factors of 2448 is 7254.
- All Factors of 2448: 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 34, 36, 48, 51, 68, 72, 102, 136, 144, 153, 204, 272, 306, 408, 612, 816, 1224 and 2448
- Prime Factors of 2448: 2, 3, 17
- Prime Factorization of 2448: 24 × 32 × 171
- Sum of Factors of 2448: 7254
1. | What Are the Factors of 2448? |
2. | Factors of 2448 by Prime Factorization |
3. | Factors of 2448 in Pairs |
4. | FAQs on Factors of 2448 |
What are Factors of 2448?
Factors of 2448 are pairs of those numbers whose products result in 2448. These factors are either prime numbers or composite numbers.
How to Find the Factors of 2448?
To find the factors of 2448, we will have to find the list of numbers that would divide 2448 without leaving any remainder.
- 2448/72 = 34; therefore, 72 is a factor of 2448 and 34 is also a factor of 2448.
- 2448/816 = 3; therefore, 816 is a factor of 2448 and 3 is also a factor of 2448.
☛ Also Check:
- Factors of 5 - The factors of 5 are 1, 5
- Factors of 11 - The factors of 11 are 1, 11
- Factors of 19 - The factors of 19 are 1, 19
- Factors of 54 - The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
- Factors of 7 - The factors of 7 are 1, 7
Factors of 2448 by Prime Factorization
- 2448 ÷ 2 = 1224
- 1224 ÷ 2 = 612
- 612 ÷ 2 = 306
- 306 ÷ 2 = 153
Further dividing 153 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 153 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 2448 can be written as 24 × 32 × 171 where 2, 3, 17 are prime.
Factors of 2448 in Pairs
Pair factors of 2448 are the pairs of numbers that when multiplied give the product 2448. The factors of 2448 in pairs are:
- 1 × 2448 = (1, 2448)
- 2 × 1224 = (2, 1224)
- 3 × 816 = (3, 816)
- 4 × 612 = (4, 612)
- 6 × 408 = (6, 408)
- 8 × 306 = (8, 306)
- 9 × 272 = (9, 272)
- 12 × 204 = (12, 204)
- 16 × 153 = (16, 153)
- 17 × 144 = (17, 144)
- 18 × 136 = (18, 136)
- 24 × 102 = (24, 102)
- 34 × 72 = (34, 72)
- 36 × 68 = (36, 68)
- 48 × 51 = (48, 51)
Negative pair factors of 2448 are:
- -1 × -2448 = (-1, -2448)
- -2 × -1224 = (-2, -1224)
- -3 × -816 = (-3, -816)
- -4 × -612 = (-4, -612)
- -6 × -408 = (-6, -408)
- -8 × -306 = (-8, -306)
- -9 × -272 = (-9, -272)
- -12 × -204 = (-12, -204)
- -16 × -153 = (-16, -153)
- -17 × -144 = (-17, -144)
- -18 × -136 = (-18, -136)
- -24 × -102 = (-24, -102)
- -34 × -72 = (-34, -72)
- -36 × -68 = (-36, -68)
- -48 × -51 = (-48, -51)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 2448 Solved Examples
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Example 1: How many factors are there for 2448?
Solution:
The factors of 2448 are too many, therefore if we can find the prime factorization of 2448, 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 2448 = 24 × 32 × 171
Therefore, the total number of factors are (4 + 1) × (2 + 1) × (1 + 1) = 5 × 3 × 2 = 30 -
Example 2: Find the LCM and Highest Common Factor (HCF) of 2448 and 1118.
Solution:
The factors of 2448 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 34, 36, 48, 51, 68, 72, 102, 136, 144, 153, 204, 272, 306, 408, 612, 816, 1224, 2448 and factors of 1118 are 1, 2, 13, 26, 43, 86, 559, 1118.
Therefore, the LCM of 2448 and 1118 is 1368432 and Highest Common Factor (HCF) of 2448 and 1118 is 2. -
Example 3: Find if 3, 17, 24, 68, 72, 102, 204 and 1826 are factors of 2448.
Solution:
When we divide 2448 by 1826 it leaves a remainder. Therefore, the number 1826 is not a factor of 2448. All numbers except 1826 are factors of 2448.
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Example 4: Find the product of all the prime factors of 2448.
Solution:
Since, the prime factors of 2448 are 2, 3, 17. Therefore, the product of prime factors = 2 × 3 × 17 = 102.
FAQs on Factors of 2448
What are the Factors of 2448?
The factors of 2448 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 34, 36, 48, 51, 68, 72, 102, 136, 144, 153, 204, 272, 306, 408, 612, 816, 1224, 2448 and its negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -16, -17, -18, -24, -34, -36, -48, -51, -68, -72, -102, -136, -144, -153, -204, -272, -306, -408, -612, -816, -1224, -2448.
What is the Sum of all Factors of 2448?
Sum of all factors of 2448 = (24 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (171 + 1 - 1)/(17 - 1) = 7254
What are Pair Factors of 2448?
The pair factors of 2448 are (1, 2448), (2, 1224), (3, 816), (4, 612), (6, 408), (8, 306), (9, 272), (12, 204), (16, 153), (17, 144), (18, 136), (24, 102), (34, 72), (36, 68), (48, 51).
What is the Greatest Common Factor of 2448 and 343?
The factors of 2448 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 34, 36, 48, 51, 68, 72, 102, 136, 144, 153, 204, 272, 306, 408, 612, 816, 1224, 2448 and the factors of 343 are 1, 7, 49, 343. 2448 and 343 have only one common factor which is 1. This implies that 2448 and 343 are co-prime.
Hence, the Greatest Common Factor (GCF) of 2448 and 343 is 1.
How Many Factors of 770 are also common to the Factors of 2448?
Since, the factors of 2448 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 34, 36, 48, 51, 68, 72, 102, 136, 144, 153, 204, 272, 306, 408, 612, 816, 1224, 2448 and the factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770.
Hence, [1, 2] are the common factors of 2448 and 770.
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