Factors of 1320
Factors of 1320 are integers that can be divided evenly into 1320. It has total 32 factors of which 1320 is the biggest factor and the prime factors of 1320 are 2, 3, 5, 11. The Prime Factorization of 1320 is 23 × 31 × 51 × 111.
- All Factors of 1320: 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 60, 66, 88, 110, 120, 132, 165, 220, 264, 330, 440, 660 and 1320
- Prime Factors of 1320: 2, 3, 5, 11
- Prime Factorization of 1320: 23 × 31 × 51 × 111
- Sum of Factors of 1320: 4320
1. | What Are the Factors of 1320? |
2. | Factors of 1320 by Prime Factorization |
3. | Factors of 1320 in Pairs |
4. | FAQs on Factors of 1320 |
What are Factors of 1320?
Factors of 1320 are pairs of those numbers whose products result in 1320. These factors are either prime numbers or composite numbers.
How to Find the Factors of 1320?
To find the factors of 1320, we will have to find the list of numbers that would divide 1320 without leaving any remainder.
- 1320/22 = 60; therefore, 22 is a factor of 1320 and 60 is also a factor of 1320.
- 1320/11 = 120; therefore, 11 is a factor of 1320 and 120 is also a factor of 1320.
☛ Also Check:
- Factors of 15 - The factors of 15 are 1, 3, 5, 15
- Factors of 108 - The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
- Factors of 19 - The factors of 19 are 1, 19
- Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 44 - The factors of 44 are 1, 2, 4, 11, 22, 44
Factors of 1320 by Prime Factorization
- 1320 ÷ 2 = 660
- 660 ÷ 2 = 330
- 330 ÷ 2 = 165
Further dividing 165 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 165 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 1320 can be written as 23 × 31 × 51 × 111 where 2, 3, 5, 11 are prime.
Factors of 1320 in Pairs
Pair factors of 1320 are the pairs of numbers that when multiplied give the product 1320. The factors of 1320 in pairs are:
- 1 × 1320 = (1, 1320)
- 2 × 660 = (2, 660)
- 3 × 440 = (3, 440)
- 4 × 330 = (4, 330)
- 5 × 264 = (5, 264)
- 6 × 220 = (6, 220)
- 8 × 165 = (8, 165)
- 10 × 132 = (10, 132)
- 11 × 120 = (11, 120)
- 12 × 110 = (12, 110)
- 15 × 88 = (15, 88)
- 20 × 66 = (20, 66)
- 22 × 60 = (22, 60)
- 24 × 55 = (24, 55)
- 30 × 44 = (30, 44)
- 33 × 40 = (33, 40)
Negative pair factors of 1320 are:
- -1 × -1320 = (-1, -1320)
- -2 × -660 = (-2, -660)
- -3 × -440 = (-3, -440)
- -4 × -330 = (-4, -330)
- -5 × -264 = (-5, -264)
- -6 × -220 = (-6, -220)
- -8 × -165 = (-8, -165)
- -10 × -132 = (-10, -132)
- -11 × -120 = (-11, -120)
- -12 × -110 = (-12, -110)
- -15 × -88 = (-15, -88)
- -20 × -66 = (-20, -66)
- -22 × -60 = (-22, -60)
- -24 × -55 = (-24, -55)
- -30 × -44 = (-30, -44)
- -33 × -40 = (-33, -40)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 1320 Solved Examples
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Example 1: How many factors are there for 1320?
Solution:
The factors of 1320 are too many, therefore if we can find the prime factorization of 1320, 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 1320 = 23 × 31 × 51 × 111
Therefore, the total number of factors are (3 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 × 2 = 32 -
Example 2: Find the LCM and Greatest Common Divisor (GCD) of 1320 and 1311.
Solution:
The factors of 1320 are 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 60, 66, 88, 110, 120, 132, 165, 220, 264, 330, 440, 660, 1320 and factors of 1311 are 1, 3, 19, 23, 57, 69, 437, 1311.
Therefore, the LCM of 1320 and 1311 is 576840 and Greatest Common Divisor (GCD) of 1320 and 1311 is 3. -
Example 3: Find if 3, 5, 20, 30, 110, 132, 440 and 1031 are factors of 1320.
Solution:
When we divide 1320 by 1031 it leaves a remainder. Therefore, the number 1031 is not a factor of 1320. All numbers except 1031 are factors of 1320.
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Example 4: Find the product of all the prime factors of 1320.
Solution:
Since, the prime factors of 1320 are 2, 3, 5, 11. Therefore, the product of prime factors = 2 × 3 × 5 × 11 = 330.
FAQs on Factors of 1320
What are the Factors of 1320?
The factors of 1320 are 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 60, 66, 88, 110, 120, 132, 165, 220, 264, 330, 440, 660, 1320 and its negative factors are -1, -2, -3, -4, -5, -6, -8, -10, -11, -12, -15, -20, -22, -24, -30, -33, -40, -44, -55, -60, -66, -88, -110, -120, -132, -165, -220, -264, -330, -440, -660, -1320.
What is the Sum of the Factors of 1320?
Sum of all factors of 1320 = (23 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (111 + 1 - 1)/(11 - 1) = 4320
What numbers are the Pair Factors of 1320?
The pair factors of 1320 are (1, 1320), (2, 660), (3, 440), (4, 330), (5, 264), (6, 220), (8, 165), (10, 132), (11, 120), (12, 110), (15, 88), (20, 66), (22, 60), (24, 55), (30, 44), (33, 40).
What is the Greatest Common Factor of 1320 and 401?
The factors of 1320 are 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 60, 66, 88, 110, 120, 132, 165, 220, 264, 330, 440, 660, 1320 and the factors of 401 are 1, 401. 1320 and 401 have only one common factor which is 1. This implies that 1320 and 401 are co-prime.
Hence, the Greatest Common Factor (GCF) of 1320 and 401 is 1.
How Many Factors of 95 are also common to the Factors of 1320?
Since, the factors of 1320 are 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 20, 22, 24, 30, 33, 40, 44, 55, 60, 66, 88, 110, 120, 132, 165, 220, 264, 330, 440, 660, 1320 and the factors of 95 are 1, 5, 19, 95.
Hence, [1, 5] are the common factors of 1320 and 95.
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