Factors of 2009
Factors of 2009 are numbers that, when multiplied in pairs give the product as 2009. It has a total of 6 factors of which 2009 is the biggest factor and the positive factors of 2009 are 1, 7, 41, 49, 287, 2009. The sum of all factors of 2009 is 2394. Its Prime Factors are 7 × 41 and (1, 2009), (7, 287), (41, 49) are Pair Factors.
- All Factors of 2009: 1, 7, 41, 49, 287 and 2009
- Negative Factors of 2009: -1, -7, -41, -49, -287 and -2009
- Prime Factors of 2009: 7, 41
- Prime Factorization of 2009: 72 × 411
- Sum of Factors of 2009: 2394
1. | What Are the Factors of 2009? |
2. | Factors of 2009 by Prime Factorization |
3. | Factors of 2009 in Pairs |
4. | FAQs on Factors of 2009 |
What are Factors of 2009?
Factors of 2009 are pairs of those numbers whose products result in 2009. These factors are either prime numbers or composite numbers.
How to Find the Factors of 2009?
To find the factors of 2009, we will have to find the list of numbers that would divide 2009 without leaving any remainder.
- 2009/1 = 2009; therefore, 1 is a factor of 2009.
- 2009/7 = 287; therefore, 7 is a factor of 2009.
☛ Also Check:
- Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- Factors of 45 - The factors of 45 are 1, 3, 5, 9, 15, 45
- Factors of 35 - The factors of 35 are 1, 5, 7, 35
- Factors of 13 - The factors of 13 are 1, 13
- Factors of 28 - The factors of 28 are 1, 2, 4, 7, 14, 28
Factors of 2009 by Prime Factorization
- 2009 ÷ 7 = 287
- 287 ÷ 7 = 41
Further dividing 41 by 7 gives a non-zero remainder. So we stop the process and continue dividing the number 41 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 2009 can be written as 72 × 411 where 7, 41 are prime.
Factors of 2009 in Pairs
Pair factors of 2009 are the pairs of numbers that when multiplied give the product 2009. The factors of 2009 in pairs are:
- 1 × 2009 = (1, 2009)
- 7 × 287 = (7, 287)
- 41 × 49 = (41, 49)
Negative pair factors of 2009 are:
- -1 × -2009 = (-1, -2009)
- -7 × -287 = (-7, -287)
- -41 × -49 = (-41, -49)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 2009 Solved Examples
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Example 1: How many factors are there for 2009?
Solution:
The factors of 2009 are 1, 7, 41, 49, 287, 2009. Therefore, 2009 has 6 factors.
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Example 2: Find the LCM and Greatest Common Divisor (GCD) of 2009 and 384.
Solution:
The factors of 2009 are 1, 7, 41, 49, 287, 2009 and factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384.
Therefore, the LCM of 2009 and 384 is 771456 and Greatest Common Divisor (GCD) of 2009 and 384 is 1. -
Example 3: Find if 1, 49, 287 and 1742 are factors of 2009.
Solution:
When we divide 2009 by 1742 it leaves a remainder. Therefore, the number 1742 is not a factor of 2009. All numbers except 1742 are factors of 2009.
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Example 4: Find the product of all the prime factors of 2009.
Solution:
Since, the prime factors of 2009 are 7, 41. Therefore, the product of prime factors = 7 × 41 = 287.
FAQs on Factors of 2009
What are the Factors of 2009?
The factors of 2009 are 1, 7, 41, 49, 287, 2009 and its negative factors are -1, -7, -41, -49, -287, -2009.
What is the Sum of all the Factors of 2009?
Since, all factors of 2009 are 1, 7, 41, 49, 287, 2009 therefore, the sum of its factors is 1 + 7 + 41 + 49 + 287 + 2009 = 2394.
What are the Prime Factors of 2009?
The prime factors of 2009 are 7, 41.
What is the Greatest Common Factor of 2009 and 994?
The factors of 2009 and 994 are 1, 7, 41, 49, 287, 2009 and 1, 2, 7, 14, 71, 142, 497, 994 respectively.
Common factors of 2009 and 994 are [1, 7].
Hence, the GCF of 2009 and 994 is 7.
How Many Factors of 2009 are also Factors of 422?
Since, the factors of 2009 are 1, 7, 41, 49, 287, 2009 and factors of 422 are 1, 2, 211, 422. Hence, 2009 and 422 have only one common factor which is 1. Therefore, 2009 and 422 are co-prime.
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