Factors of 1620
Factors of 1620 are numbers that, when multiplied in pairs give the product as 1620. There are 30 factors of 1620 of which 1620 itself is the biggest factor and its prime factors are 2, 3, 5 The Prime Factorization of 1620 is 22 × 34 × 51.
- All Factors of 1620: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810 and 1620
- Prime Factors of 1620: 2, 3, 5
- Prime Factorization of 1620: 22 × 34 × 51
- Sum of Factors of 1620: 5082
1. | What Are the Factors of 1620? |
2. | Factors of 1620 by Prime Factorization |
3. | Factors of 1620 in Pairs |
4. | FAQs on Factors of 1620 |
What are Factors of 1620?
Factors of 1620 are pairs of those numbers whose products result in 1620. These factors are either prime numbers or composite numbers.
How to Find the Factors of 1620?
To find the factors of 1620, we will have to find the list of numbers that would divide 1620 without leaving any remainder.
- 1620/1 = 1620; therefore, 1 is a factor of 1620.
- 1620/270 = 6; therefore, 270 is a factor of 1620.
☛ Also Check:
- Factors of 20 - The factors of 20 are 1, 2, 4, 5, 10, 20
- Factors of 57 - The factors of 57 are 1, 3, 19, 57
- Factors of 15 - The factors of 15 are 1, 3, 5, 15
- Factors of 55 - The factors of 55 are 1, 5, 11, 55
- Factors of 22 - The factors of 22 are 1, 2, 11, 22
Factors of 1620 by Prime Factorization
- 1620 ÷ 2 = 810
- 810 ÷ 2 = 405
Further dividing 405 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 405 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 1620 can be written as 22 × 34 × 51 where 2, 3, 5 are prime.
Factors of 1620 in Pairs
Pair factors of 1620 are the pairs of numbers that when multiplied give the product 1620. The factors of 1620 in pairs are:
- 1 × 1620 = (1, 1620)
- 2 × 810 = (2, 810)
- 3 × 540 = (3, 540)
- 4 × 405 = (4, 405)
- 5 × 324 = (5, 324)
- 6 × 270 = (6, 270)
- 9 × 180 = (9, 180)
- 10 × 162 = (10, 162)
- 12 × 135 = (12, 135)
- 15 × 108 = (15, 108)
- 18 × 90 = (18, 90)
- 20 × 81 = (20, 81)
- 27 × 60 = (27, 60)
- 30 × 54 = (30, 54)
- 36 × 45 = (36, 45)
Negative pair factors of 1620 are:
- -1 × -1620 = (-1, -1620)
- -2 × -810 = (-2, -810)
- -3 × -540 = (-3, -540)
- -4 × -405 = (-4, -405)
- -5 × -324 = (-5, -324)
- -6 × -270 = (-6, -270)
- -9 × -180 = (-9, -180)
- -10 × -162 = (-10, -162)
- -12 × -135 = (-12, -135)
- -15 × -108 = (-15, -108)
- -18 × -90 = (-18, -90)
- -20 × -81 = (-20, -81)
- -27 × -60 = (-27, -60)
- -30 × -54 = (-30, -54)
- -36 × -45 = (-36, -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 1620 Solved Examples
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Example 1: How many factors are there for 1620?
Solution:
The factors of 1620 are too many, therefore if we can find the prime factorization of 1620, 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 1620 = 22 × 34 × 51
Therefore, the total number of factors are (2 + 1) × (4 + 1) × (1 + 1) = 3 × 5 × 2 = 30 -
Example 2: Find the Least Common Multiple and Greatest Common Factor (GCF) of 1620 and 1323.
Solution:
The factors of 1620 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620 and factors of 1323 are 1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441, 1323.
Therefore, the Least Common Multiple of 1620 and 1323 is 79380 and Greatest Common Factor (GCF) of 1620 and 1323 is 27. -
Example 3: Find if 9, 10, 15, 20, 162, 324, 540 and 1116 are factors of 1620.
Solution:
When we divide 1620 by 1116 it leaves a remainder. Therefore, the number 1116 is not a factor of 1620. All numbers except 1116 are factors of 1620.
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Example 4: Find the product of all the prime factors of 1620.
Solution:
Since, the prime factors of 1620 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.
FAQs on Factors of 1620
What are the Factors of 1620?
The factors of 1620 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620 and its negative factors are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -27, -30, -36, -45, -54, -60, -81, -90, -108, -135, -162, -180, -270, -324, -405, -540, -810, -1620.
What is the Sum of the Factors of 1620?
Sum of all factors of 1620 = (22 + 1 - 1)/(2 - 1) × (34 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) = 5082
What are the Prime Factors of 1620?
The prime factors of 1620 are 2, 3, 5.
What is the Greatest Common Factor of 1620 and 673?
The factors of 1620 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620 and the factors of 673 are 1, 673. 1620 and 673 have only one common factor which is 1. This implies that 1620 and 673 are co-prime.
Hence, the Greatest Common Factor (GCF) of 1620 and 673 is 1.
How Many Factors of 1620 are also Factors of 1150?
Since, the factors of 1620 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 162, 180, 270, 324, 405, 540, 810, 1620 and the factors of 1150 are 1, 2, 5, 10, 23, 25, 46, 50, 115, 230, 575, 1150.
Hence, [1, 2, 5, 10] are the common factors of 1620 and 1150.
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