Factors of 186
Factors of 186 are the list of integers that can be evenly divided into 186. There are overall 8 factors of 186 i.e. 1, 2, 3, 6, 31, 62, 93, 186 where 186 is the biggest factor. The sum of all factors of 186 is 384. Its Prime Factors are 2 × 3 × 31 and (1, 186), (2, 93), (3, 62), (6, 31) are Pair Factors.
- All Factors of 186: 1, 2, 3, 6, 31, 62, 93 and 186
- Negative Factors of 186: -1, -2, -3, -6, -31, -62, -93 and -186
- Prime Factors of 186: 2, 3, 31
- Prime Factorization of 186: 21 × 31 × 311
- Sum of Factors of 186: 384
1. | What Are the Factors of 186? |
2. | Factors of 186 by Prime Factorization |
3. | Factors of 186 in Pairs |
4. | FAQs on Factors of 186 |
What are Factors of 186?
Factors of 186 are pairs of those numbers whose products result in 186. These factors are either prime numbers or composite numbers.
How to Find the Factors of 186?
To find the factors of 186, we will have to find the list of numbers that would divide 186 without leaving any remainder.
- 186/62 = 3; therefore, 62 is a factor of 186 and 3 is also a factor of 186.
- 186/31 = 6; therefore, 31 is a factor of 186 and 6 is also a factor of 186.
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- Factors of 90 - The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
- Factors of 45 - The factors of 45 are 1, 3, 5, 9, 15, 45
- Factors of 65 - The factors of 65 are 1, 5, 13, 65
Factors of 186 by Prime Factorization
- 186 ÷ 2 = 93
Further dividing 93 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 93 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 186 can be written as 21 × 31 × 311 where 2, 3, 31 are prime.
Factors of 186 in Pairs
Pair factors of 186 are the pairs of numbers that when multiplied give the product 186. The factors of 186 in pairs are:
- 1 × 186 = (1, 186)
- 2 × 93 = (2, 93)
- 3 × 62 = (3, 62)
- 6 × 31 = (6, 31)
Negative pair factors of 186 are:
- -1 × -186 = (-1, -186)
- -2 × -93 = (-2, -93)
- -3 × -62 = (-3, -62)
- -6 × -31 = (-6, -31)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 186 Solved Examples
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Example 1: How many factors are there for 186?
Solution:
The factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186. Therefore, 186 has 8 factors.
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Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 186 and 143.
Solution:
The factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186 and factors of 143 are 1, 11, 13, 143.
Therefore, the Least Common Multiple (LCM) of 186 and 143 is 26598 and Highest Common Factor (HCF) of 186 and 143 is 1. -
Example 3: Find if 1, 31, 93, 182 and 186 are factors of 186.
Solution:
When we divide 186 by 182 it leaves a remainder. Therefore, the number 182 is not a factor of 186. All numbers except 182 are factors of 186.
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Example 4: Find the product of all the prime factors of 186.
Solution:
Since, the prime factors of 186 are 2, 3, 31. Therefore, the product of prime factors = 2 × 3 × 31 = 186.
FAQs on Factors of 186
What are the Factors of 186?
The factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186 and its negative factors are -1, -2, -3, -6, -31, -62, -93, -186.
What is the Sum of Factors of 186?
Sum of all factors of 186 = (21 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (311 + 1 - 1)/(31 - 1) = 384
What are Prime Factors of 186?
The prime factors of 186 are 2, 3, 31.
What is the Greatest Common Factor of 186 and 45?
The factors of 186 and 45 are 1, 2, 3, 6, 31, 62, 93, 186 and 1, 3, 5, 9, 15, 45 respectively.
Common factors of 186 and 45 are [1, 3].
Hence, the Greatest Common Factor of 186 and 45 is 3.
What are the Common Factors of 186 and 159?
Since, the factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186 and the factors of 159 are 1, 3, 53, 159.
Hence, [1, 3] are the common factors of 186 and 159.
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