Factors of 2020
Factors of 2020 are the list of integers that we can split evenly into 2020. There are 12 factors of 2020, of which the following are its prime factors 2, 5, 101. The Prime Factorization of 2020 is 22 × 51 × 1011.
- All Factors of 2020: 1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010 and 2020
- Prime Factors of 2020: 2, 5, 101
- Prime Factorization of 2020: 22 × 51 × 1011
- Sum of Factors of 2020: 4284
1. | What Are the Factors of 2020? |
2. | Factors of 2020 by Prime Factorization |
3. | Factors of 2020 in Pairs |
4. | FAQs on Factors of 2020 |
What are Factors of 2020?
Factors of 2020 are pairs of those numbers whose products result in 2020. These factors are either prime numbers or composite numbers.
How to Find the Factors of 2020?
To find the factors of 2020, we will have to find the list of numbers that would divide 2020 without leaving any remainder.
- 2020/101 = 20; therefore, 101 is a factor of 2020 and 20 is also a factor of 2020.
- 2020/2 = 1010; therefore, 2 is a factor of 2020 and 1010 is also a factor of 2020.
☛ Also Check:
- Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
- Factors of 50 - The factors of 50 are 1, 2, 5, 10, 25, 50
- Factors of 29 - The factors of 29 are 1, 29
- Factors of 180 - The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
- Factors of 13 - The factors of 13 are 1, 13
Factors of 2020 by Prime Factorization
- 2020 ÷ 2 = 1010
- 1010 ÷ 2 = 505
Further dividing 505 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 505 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 2020 can be written as 22 × 51 × 1011 where 2, 5, 101 are prime.
Factors of 2020 in Pairs
Pair factors of 2020 are the pairs of numbers that when multiplied give the product 2020. The factors of 2020 in pairs are:
- 1 × 2020 = (1, 2020)
- 2 × 1010 = (2, 1010)
- 4 × 505 = (4, 505)
- 5 × 404 = (5, 404)
- 10 × 202 = (10, 202)
- 20 × 101 = (20, 101)
Negative pair factors of 2020 are:
- -1 × -2020 = (-1, -2020)
- -2 × -1010 = (-2, -1010)
- -4 × -505 = (-4, -505)
- -5 × -404 = (-5, -404)
- -10 × -202 = (-10, -202)
- -20 × -101 = (-20, -101)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 2020 Solved Examples
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Example 1: How many factors are there for 2020?
Solution:
The factors of 2020 are too many, therefore if we can find the prime factorization of 2020, 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 2020 = 22 × 51 × 1011
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12 -
Example 2: Find the LCM and Greatest Common Factor (GCF) of 2020 and 1829.
Solution:
The factors of 2020 are 1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010, 2020 and factors of 1829 are 1, 31, 59, 1829.
Therefore, the LCM of 2020 and 1829 is 3694580 and Greatest Common Factor (GCF) of 2020 and 1829 is 1. -
Example 3: Find if 1, 10, 20, 202, 505, 1814 and 2020 are factors of 2020.
Solution:
When we divide 2020 by 1814 it leaves a remainder. Therefore, the number 1814 is not a factor of 2020. All numbers except 1814 are factors of 2020.
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Example 4: Find the product of all the prime factors of 2020.
Solution:
Since, the prime factors of 2020 are 2, 5, 101. Therefore, the product of prime factors = 2 × 5 × 101 = 1010.
FAQs on Factors of 2020
What are the Factors of 2020?
The factors of 2020 are 1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010, 2020 and its negative factors are -1, -2, -4, -5, -10, -20, -101, -202, -404, -505, -1010, -2020.
What is the Sum of all Factors of 2020?
Sum of all factors of 2020 = (22 + 1 - 1)/(2 - 1) × (51 + 1 - 1)/(5 - 1) × (1011 + 1 - 1)/(101 - 1) = 4284
What are Prime Factors of 2020?
The prime factors of 2020 are 2, 5, 101.
What is the Greatest Common Factor of 2020 and 1640?
The factors of 2020 and 1640 are 1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010, 2020 and 1, 2, 4, 5, 8, 10, 20, 40, 41, 82, 164, 205, 328, 410, 820, 1640 respectively.
Common factors of 2020 and 1640 are [1, 2, 4, 5, 10, 20].
Hence, the Greatest Common Factor (GCF) of 2020 and 1640 is 20.
How Many Factors of 2020 are also Factors of 376?
Since, the factors of 2020 are 1, 2, 4, 5, 10, 20, 101, 202, 404, 505, 1010, 2020 and the factors of 376 are 1, 2, 4, 8, 47, 94, 188, 376.
Hence, [1, 2, 4] are the common factors of 2020 and 376.
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