Factors of 165
Factors of 165 are the list of integers that we can split evenly into 165. There are 8 factors of 165 of which 165 itself is the biggest factor and its positive factors are 1, 3, 5, 11, 15, 33, 55, 165. The sum of all factors of 165 is 288. Its Prime Factors are 3 × 5 × 11 and (1, 165), (3, 55), (5, 33), (11, 15) are Pair Factors.
- All Factors of 165: 1, 3, 5, 11, 15, 33, 55 and 165
- Negative Factors of 165: -1, -3, -5, -11, -15, -33, -55 and -165
- Prime Factors of 165: 3, 5, 11
- Prime Factorization of 165: 31 × 51 × 111
- Sum of Factors of 165: 288
1. | What Are the Factors of 165? |
2. | Factors of 165 by Prime Factorization |
3. | Factors of 165 in Pairs |
4. | FAQs on Factors of 165 |
What are Factors of 165?
Factors of 165 are pairs of those numbers whose products result in 165. These factors are either prime numbers or composite numbers.
How to Find the Factors of 165?
To find the factors of 165, we will have to find the list of numbers that would divide 165 without leaving any remainder.
- 165/3 = 55; therefore, 3 is a factor of 165 and 55 is also a factor of 165.
- 165/15 = 11; therefore, 15 is a factor of 165 and 11 is also a factor of 165.
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- Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 50 - The factors of 50 are 1, 2, 5, 10, 25, 50
- Factors of 128 - The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128
Factors of 165 by Prime Factorization
- 165 ÷ 3 = 55
Further dividing 55 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 55 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 165 can be written as 31 × 51 × 111 where 3, 5, 11 are prime.
Factors of 165 in Pairs
Pair factors of 165 are the pairs of numbers that when multiplied give the product 165. The factors of 165 in pairs are:
- 1 × 165 = (1, 165)
- 3 × 55 = (3, 55)
- 5 × 33 = (5, 33)
- 11 × 15 = (11, 15)
Negative pair factors of 165 are:
- -1 × -165 = (-1, -165)
- -3 × -55 = (-3, -55)
- -5 × -33 = (-5, -33)
- -11 × -15 = (-11, -15)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 165 Solved Examples
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Example 1: How many factors are there for 165?
Solution:
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165. Therefore, 165 has 8 factors.
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Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 165 and 76.
Solution:
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165 and factors of 76 are 1, 2, 4, 19, 38, 76.
Therefore, the Lowest Common Multiple (LCM) of 165 and 76 is 12540 and Greatest Common Divisor (GCD) of 165 and 76 is 1. -
Example 3: Find if 11, 33, 38, 55 and 165 are factors of 165.
Solution:
When we divide 165 by 38 it leaves a remainder. Therefore, the number 38 is not a factor of 165. All numbers except 38 are factors of 165.
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Example 4: Find the product of all the prime factors of 165.
Solution:
Since, the prime factors of 165 are 3, 5, 11. Therefore, the product of prime factors = 3 × 5 × 11 = 165.
FAQs on Factors of 165
What are the Factors of 165?
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165 and its negative factors are -1, -3, -5, -11, -15, -33, -55, -165.
What is the Sum of the Factors of 165?
Sum of all factors of 165 = (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (111 + 1 - 1)/(11 - 1) = 288
What are Prime Factors of 165?
The prime factors of 165 are 3, 5, 11.
What is the Greatest Common Factor of 165 and 90?
The factors of 165 and 90 are 1, 3, 5, 11, 15, 33, 55, 165 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 respectively.
Common factors of 165 and 90 are [1, 3, 5, 15].
Hence, the Greatest Common Factor (GCF) of 165 and 90 is 15.
How Many Factors of 165 are also common to the Factors of 22?
Since, the factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165 and the factors of 22 are 1, 2, 11, 22.
Hence, [1, 11] are the common factors of 165 and 22.
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