Factors of 340
Factors of 340 are integers that can be divided evenly into 340. There are overall 12 factors of 340 among which 340 is the biggest factor and 2, 5, 17 are its prime factors. The sum of all factors of 340 is 756.
- All Factors of 340: 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170 and 340
- Prime Factors of 340: 2, 5, 17
- Prime Factorization of 340: 22 × 51 × 171
- Sum of Factors of 340: 756
1. | What Are the Factors of 340? |
2. | Factors of 340 by Prime Factorization |
3. | Factors of 340 in Pairs |
4. | FAQs on Factors of 340 |
What are Factors of 340?
Factors of 340 are pairs of those numbers whose products result in 340. These factors are either prime numbers or composite numbers.
How to Find the Factors of 340?
To find the factors of 340, we will have to find the list of numbers that would divide 340 without leaving any remainder.
- 340/34 = 10; therefore, 34 is a factor of 340 and 10 is also a factor of 340.
- 340/170 = 2; therefore, 170 is a factor of 340 and 2 is also a factor of 340.
☛ Also Check:
- Factors of 39 - The factors of 39 are 1, 3, 13, 39
- Factors of 121 - The factors of 121 are 1, 11, 121
- Factors of 9 - The factors of 9 are 1, 3, 9
- 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 80 - The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Factors of 340 by Prime Factorization
- 340 ÷ 2 = 170
- 170 ÷ 2 = 85
Further dividing 85 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 85 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 340 can be written as 22 × 51 × 171 where 2, 5, 17 are prime.
Factors of 340 in Pairs
Pair factors of 340 are the pairs of numbers that when multiplied give the product 340. The factors of 340 in pairs are:
- 1 × 340 = (1, 340)
- 2 × 170 = (2, 170)
- 4 × 85 = (4, 85)
- 5 × 68 = (5, 68)
- 10 × 34 = (10, 34)
- 17 × 20 = (17, 20)
Negative pair factors of 340 are:
- -1 × -340 = (-1, -340)
- -2 × -170 = (-2, -170)
- -4 × -85 = (-4, -85)
- -5 × -68 = (-5, -68)
- -10 × -34 = (-10, -34)
- -17 × -20 = (-17, -20)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 340 Solved Examples
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Example 1: How many factors are there for 340?
Solution:
The factors of 340 are too many, therefore if we can find the prime factorization of 340, 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 340 = 22 × 51 × 171
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 Highest Common Factor (HCF) of 340 and 313.
Solution:
The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340 and factors of 313 are 1, 313.
Therefore, the Least Common Multiple (LCM) of 340 and 313 is 106420 and Highest Common Factor (HCF) of 340 and 313 is 1. -
Example 3: Find if 2, 4, 10, 17, 47, 68 and 170 are factors of 340.
Solution:
When we divide 340 by 47 it leaves a remainder. Therefore, the number 47 is not a factor of 340. All numbers except 47 are factors of 340.
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Example 4: Find the product of all the prime factors of 340.
Solution:
Since, the prime factors of 340 are 2, 5, 17. Therefore, the product of prime factors = 2 × 5 × 17 = 170.
FAQs on Factors of 340
What are the Factors of 340?
The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340 and its negative factors are -1, -2, -4, -5, -10, -17, -20, -34, -68, -85, -170, -340.
What is the Sum of the Factors of 340?
Sum of all factors of 340 = (22 + 1 - 1)/(2 - 1) × (51 + 1 - 1)/(5 - 1) × (171 + 1 - 1)/(17 - 1) = 756
What are Prime Factors of 340?
The prime factors of 340 are 2, 5, 17.
What is the Greatest Common Factor of 340 and 289?
The factors of 340 and 289 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340 and 1, 17, 289 respectively.
Common factors of 340 and 289 are [1, 17].
Hence, the GCF of 340 and 289 is 17.
What are the Common Factors of 340 and 274?
Since, the factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340 and the factors of 274 are 1, 2, 137, 274.
Hence, [1, 2] are the common factors of 340 and 274.
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