Factors of 1980
Factors of 1980 are numbers that, when multiplied in pairs give the product as 1980. It has total 36 factors of which 1980 is the biggest factor and the prime factors of 1980 are 2, 3, 5, 11. The Prime Factorization of 1980 is 22 × 32 × 51 × 111.
- All Factors of 1980: 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990 and 1980
- Prime Factors of 1980: 2, 3, 5, 11
- Prime Factorization of 1980: 22 × 32 × 51 × 111
- Sum of Factors of 1980: 6552
1. | What Are the Factors of 1980? |
2. | Factors of 1980 by Prime Factorization |
3. | Factors of 1980 in Pairs |
4. | FAQs on Factors of 1980 |
What are Factors of 1980?
Factors of 1980 are pairs of those numbers whose products result in 1980. These factors are either prime numbers or composite numbers.
How to Find the Factors of 1980?
To find the factors of 1980, we will have to find the list of numbers that would divide 1980 without leaving any remainder.
- 1980/9 = 220; therefore, 9 is a factor of 1980 and 220 is also a factor of 1980.
- 1980/55 = 36; therefore, 55 is a factor of 1980 and 36 is also a factor of 1980.
☛ Also Check:
- Factors of 17 - The factors of 17 are 1, 17
- Factors of 121 - The factors of 121 are 1, 11, 121
- Factors of 35 - The factors of 35 are 1, 5, 7, 35
- Factors of 57 - The factors of 57 are 1, 3, 19, 57
- Factors of 23 - The factors of 23 are 1, 23
Factors of 1980 by Prime Factorization
- 1980 ÷ 2 = 990
- 990 ÷ 2 = 495
Further dividing 495 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 495 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 1980 can be written as 22 × 32 × 51 × 111 where 2, 3, 5, 11 are prime.
Factors of 1980 in Pairs
Pair factors of 1980 are the pairs of numbers that when multiplied give the product 1980. The factors of 1980 in pairs are:
- 1 × 1980 = (1, 1980)
- 2 × 990 = (2, 990)
- 3 × 660 = (3, 660)
- 4 × 495 = (4, 495)
- 5 × 396 = (5, 396)
- 6 × 330 = (6, 330)
- 9 × 220 = (9, 220)
- 10 × 198 = (10, 198)
- 11 × 180 = (11, 180)
- 12 × 165 = (12, 165)
- 15 × 132 = (15, 132)
- 18 × 110 = (18, 110)
- 20 × 99 = (20, 99)
- 22 × 90 = (22, 90)
- 30 × 66 = (30, 66)
- 33 × 60 = (33, 60)
- 36 × 55 = (36, 55)
- 44 × 45 = (44, 45)
Negative pair factors of 1980 are:
- -1 × -1980 = (-1, -1980)
- -2 × -990 = (-2, -990)
- -3 × -660 = (-3, -660)
- -4 × -495 = (-4, -495)
- -5 × -396 = (-5, -396)
- -6 × -330 = (-6, -330)
- -9 × -220 = (-9, -220)
- -10 × -198 = (-10, -198)
- -11 × -180 = (-11, -180)
- -12 × -165 = (-12, -165)
- -15 × -132 = (-15, -132)
- -18 × -110 = (-18, -110)
- -20 × -99 = (-20, -99)
- -22 × -90 = (-22, -90)
- -30 × -66 = (-30, -66)
- -33 × -60 = (-33, -60)
- -36 × -55 = (-36, -55)
- -44 × -45 = (-44, -45)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 1980 Solved Examples
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Example 1: How many factors are there for 1980?
Solution:
The factors of 1980 are too many, therefore if we can find the prime factorization of 1980, 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 1980 = 22 × 32 × 51 × 111
Therefore, the total number of factors are (2 + 1) × (2 + 1) × (1 + 1) × (1 + 1) = 3 × 3 × 2 × 2 = 36 -
Example 2: Find the LCM and Greatest Common Divisor (GCD) of 1980 and 240.
Solution:
The factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980 and factors of 240 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240.
Therefore, the LCM of 1980 and 240 is 7920 and Greatest Common Divisor (GCD) of 1980 and 240 is 60. -
Example 3: Find if 1, 6, 30, 33, 60, 90, 220 and 226 are factors of 1980.
Solution:
When we divide 1980 by 226 it leaves a remainder. Therefore, the number 226 is not a factor of 1980. All numbers except 226 are factors of 1980.
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Example 4: Find the product of all the prime factors of 1980.
Solution:
Since, the prime factors of 1980 are 2, 3, 5, 11. Therefore, the product of prime factors = 2 × 3 × 5 × 11 = 330.
FAQs on Factors of 1980
What are the Factors of 1980?
The factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980 and its negative factors are -1, -2, -3, -4, -5, -6, -9, -10, -11, -12, -15, -18, -20, -22, -30, -33, -36, -44, -45, -55, -60, -66, -90, -99, -110, -132, -165, -180, -198, -220, -330, -396, -495, -660, -990, -1980.
What is the Sum of all Factors of 1980?
Sum of all factors of 1980 = (22 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (111 + 1 - 1)/(11 - 1) = 6552
What are the Prime Factors of 1980?
The prime factors of 1980 are 2, 3, 5, 11.
What is the Greatest Common Factor of 1980 and 497?
The factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980 and the factors of 497 are 1, 7, 71, 497. 1980 and 497 have only one common factor which is 1. This implies that 1980 and 497 are co-prime.
Hence, the Greatest Common Factor (GCF) of 1980 and 497 is 1.
What are the Common Factors of 1980 and 545?
Since, the factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980 and the factors of 545 are 1, 5, 109, 545.
Hence, [1, 5] are the common factors of 1980 and 545.
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