Factors of 230
Factors of 230 are numbers that, when multiplied in pairs give the product as 230. There are overall 8 factors of 230 among which 230 is the biggest factor and 1, 2, 5, 10, 23, 46, 115, 230 are positive factors. The Prime Factors of 230 are 2 × 5 × 23 and its Factors in Pairs are (1, 230), (2, 115), (5, 46), (10, 23).
- All Factors of 230: 1, 2, 5, 10, 23, 46, 115 and 230
- Negative Factors of 230: -1, -2, -5, -10, -23, -46, -115 and -230
- Prime Factors of 230: 2, 5, 23
- Prime Factorization of 230: 21 × 51 × 231
- Sum of Factors of 230: 432
1. | What Are the Factors of 230? |
2. | Factors of 230 by Prime Factorization |
3. | Factors of 230 in Pairs |
4. | FAQs on Factors of 230 |
What are Factors of 230?
Factors of 230 are pairs of those numbers whose products result in 230. These factors are either prime numbers or composite numbers.
How to Find the Factors of 230?
To find the factors of 230, we will have to find the list of numbers that would divide 230 without leaving any remainder.
- 230/115 = 2; therefore, 115 is a factor of 230 and 2 is also a factor of 230.
- 230/46 = 5; therefore, 46 is a factor of 230 and 5 is also a factor of 230.
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Factors of 230 by Prime Factorization
- 230 ÷ 2 = 115
Further dividing 115 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 115 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 230 can be written as 21 × 51 × 231 where 2, 5, 23 are prime.
Factors of 230 in Pairs
Pair factors of 230 are the pairs of numbers that when multiplied give the product 230. The factors of 230 in pairs are:
- 1 × 230 = (1, 230)
- 2 × 115 = (2, 115)
- 5 × 46 = (5, 46)
- 10 × 23 = (10, 23)
Negative pair factors of 230 are:
- -1 × -230 = (-1, -230)
- -2 × -115 = (-2, -115)
- -5 × -46 = (-5, -46)
- -10 × -23 = (-10, -23)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 230 Solved Examples
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Example 1: How many factors are there for 230?
Solution:
The factors of 230 are 1, 2, 5, 10, 23, 46, 115, 230. Therefore, 230 has 8 factors.
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Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 230 and 68.
Solution:
The factors of 230 are 1, 2, 5, 10, 23, 46, 115, 230 and factors of 68 are 1, 2, 4, 17, 34, 68.
Therefore, the Least Common Multiple of 230 and 68 is 7820 and Greatest Common Divisor (GCD) of 230 and 68 is 2. -
Example 3: Find if 1, 2, 5, 90 and 230 are factors of 230.
Solution:
When we divide 230 by 90 it leaves a remainder. Therefore, the number 90 is not a factor of 230. All numbers except 90 are factors of 230.
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Example 4: Find the product of all the prime factors of 230.
Solution:
Since, the prime factors of 230 are 2, 5, 23. Therefore, the product of prime factors = 2 × 5 × 23 = 230.
FAQs on Factors of 230
What are the Factors of 230?
The factors of 230 are 1, 2, 5, 10, 23, 46, 115, 230 and its negative factors are -1, -2, -5, -10, -23, -46, -115, -230.
What is the Sum of all the Factors of 230?
Sum of all factors of 230 = (21 + 1 - 1)/(2 - 1) × (51 + 1 - 1)/(5 - 1) × (231 + 1 - 1)/(23 - 1) = 432
What are Prime Factors of 230?
The prime factors of 230 are 2, 5, 23.
What is the Greatest Common Factor of 230 and 188?
The factors of 230 and 188 are 1, 2, 5, 10, 23, 46, 115, 230 and 1, 2, 4, 47, 94, 188 respectively.
Common factors of 230 and 188 are [1, 2].
Hence, the Greatest Common Factor (GCF) of 230 and 188 is 2.
What are the Common Factors of 230 and 228?
Since, the factors of 230 are 1, 2, 5, 10, 23, 46, 115, 230 and the factors of 228 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228.
Hence, [1, 2] are the common factors of 230 and 228.
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