Factors of 580
Factors of 580 are the list of integers that can be evenly divided into 580. It has total 12 factors of which 580 is the biggest factor and the prime factors of 580 are 2, 5, 29. The Prime Factorization of 580 is 22 × 51 × 291.
- All Factors of 580: 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290 and 580
- Prime Factors of 580: 2, 5, 29
- Prime Factorization of 580: 22 × 51 × 291
- Sum of Factors of 580: 1260
1. | What Are the Factors of 580? |
2. | Factors of 580 by Prime Factorization |
3. | Factors of 580 in Pairs |
4. | FAQs on Factors of 580 |
What are Factors of 580?
Factors of 580 are pairs of those numbers whose products result in 580. These factors are either prime numbers or composite numbers.
How to Find the Factors of 580?
To find the factors of 580, we will have to find the list of numbers that would divide 580 without leaving any remainder.
- 580/2 = 290; therefore, 2 is a factor of 580 and 290 is also a factor of 580.
- 580/145 = 4; therefore, 145 is a factor of 580 and 4 is also a factor of 580.
☛ Also Check:
- Factors of 31 - The factors of 31 are 1, 31
- Factors of 13 - The factors of 13 are 1, 13
- Factors of 42 - The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 39 - The factors of 39 are 1, 3, 13, 39
- Factors of 29 - The factors of 29 are 1, 29
Factors of 580 by Prime Factorization
- 580 ÷ 2 = 290
- 290 ÷ 2 = 145
Further dividing 145 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 145 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 580 can be written as 22 × 51 × 291 where 2, 5, 29 are prime.
Factors of 580 in Pairs
Pair factors of 580 are the pairs of numbers that when multiplied give the product 580. The factors of 580 in pairs are:
- 1 × 580 = (1, 580)
- 2 × 290 = (2, 290)
- 4 × 145 = (4, 145)
- 5 × 116 = (5, 116)
- 10 × 58 = (10, 58)
- 20 × 29 = (20, 29)
Negative pair factors of 580 are:
- -1 × -580 = (-1, -580)
- -2 × -290 = (-2, -290)
- -4 × -145 = (-4, -145)
- -5 × -116 = (-5, -116)
- -10 × -58 = (-10, -58)
- -20 × -29 = (-20, -29)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 580 Solved Examples
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Example 1: How many factors are there for 580?
Solution:
The factors of 580 are too many, therefore if we can find the prime factorization of 580, 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 580 = 22 × 51 × 291
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12 -
Example 2: Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of 580 and 469.
Solution:
The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580 and factors of 469 are 1, 7, 67, 469.
Therefore, the Least Common Multiple (LCM) of 580 and 469 is 272020 and Greatest Common Factor (GCF) of 580 and 469 is 1. -
Example 3: Find if 4, 10, 29, 116, 145, 553 and 580 are factors of 580.
Solution:
When we divide 580 by 553 it leaves a remainder. Therefore, the number 553 is not a factor of 580. All numbers except 553 are factors of 580.
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Example 4: Find the product of all the prime factors of 580.
Solution:
Since, the prime factors of 580 are 2, 5, 29. Therefore, the product of prime factors = 2 × 5 × 29 = 290.
FAQs on Factors of 580
What are the Factors of 580?
The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580 and its negative factors are -1, -2, -4, -5, -10, -20, -29, -58, -116, -145, -290, -580.
What is the Sum of the Factors of 580?
Sum of all factors of 580 = (22 + 1 - 1)/(2 - 1) × (51 + 1 - 1)/(5 - 1) × (291 + 1 - 1)/(29 - 1) = 1260
What are the Prime Factors of 580?
The prime factors of 580 are 2, 5, 29.
What is the Greatest Common Factor of 580 and 53?
The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580 and the factors of 53 are 1, 53. 580 and 53 have only one common factor which is 1. This implies that 580 and 53 are co-prime.
Hence, the Greatest Common Factor (GCF) of 580 and 53 is 1.
What are the Common Factors of 580 and 318?
Since, the factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580 and the factors of 318 are 1, 2, 3, 6, 53, 106, 159, 318.
Hence, [1, 2] are the common factors of 580 and 318.
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