Factors of 495
Factors of 495 are the list of integers that we can split evenly into 495. There are 12 factors of 495 of which 495 itself is the biggest factor and its prime factors are 3, 5, 11 The sum of all factors of 495 is 936.
- All Factors of 495: 1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165 and 495
- Prime Factors of 495: 3, 5, 11
- Prime Factorization of 495: 32 × 51 × 111
- Sum of Factors of 495: 936
1. | What Are the Factors of 495? |
2. | Factors of 495 by Prime Factorization |
3. | Factors of 495 in Pairs |
4. | FAQs on Factors of 495 |
What are Factors of 495?
Factors of 495 are pairs of those numbers whose products result in 495. These factors are either prime numbers or composite numbers.
How to Find the Factors of 495?
To find the factors of 495, we will have to find the list of numbers that would divide 495 without leaving any remainder.
- 495/495 = 1; therefore, 495 is a factor of 495.
- 495/45 = 11; therefore, 45 is a factor of 495.
☛ Also Check:
- Factors of 50 - The factors of 50 are 1, 2, 5, 10, 25, 50
- Factors of 9 - The factors of 9 are 1, 3, 9
- Factors of 14 - The factors of 14 are 1, 2, 7, 14
- Factors of 49 - The factors of 49 are 1, 7, 49
- Factors of 108 - The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Factors of 495 by Prime Factorization
- 495 ÷ 3 = 165
- 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 495 can be written as 32 × 51 × 111 where 3, 5, 11 are prime.
Factors of 495 in Pairs
Pair factors of 495 are the pairs of numbers that when multiplied give the product 495. The factors of 495 in pairs are:
- 1 × 495 = (1, 495)
- 3 × 165 = (3, 165)
- 5 × 99 = (5, 99)
- 9 × 55 = (9, 55)
- 11 × 45 = (11, 45)
- 15 × 33 = (15, 33)
Negative pair factors of 495 are:
- -1 × -495 = (-1, -495)
- -3 × -165 = (-3, -165)
- -5 × -99 = (-5, -99)
- -9 × -55 = (-9, -55)
- -11 × -45 = (-11, -45)
- -15 × -33 = (-15, -33)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 495 Solved Examples
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Example 1: How many factors are there for 495?
Solution:
The factors of 495 are too many, therefore if we can find the prime factorization of 495, 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 495 = 32 × 51 × 111
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12 -
Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 495 and 239.
Solution:
The factors of 495 are 1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, 495 and factors of 239 are 1, 239.
Therefore, the Least Common Multiple of 495 and 239 is 118305 and Greatest Common Divisor (GCD) of 495 and 239 is 1. -
Example 3: Find if 3, 9, 33, 45, 99, 165 and 495 are factors of 495.
Solution:
When we divide 495 by 3, 9, 33, 45, 99, 165, 495 it doesn't leave any remainder. Therefore, 3, 9, 33, 45, 99, 165, 495 are factors of 495.
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Example 4: Find the product of all the prime factors of 495.
Solution:
Since, the prime factors of 495 are 3, 5, 11. Therefore, the product of prime factors = 3 × 5 × 11 = 165.
FAQs on Factors of 495
What are the Factors of 495?
The factors of 495 are 1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, 495 and its negative factors are -1, -3, -5, -9, -11, -15, -33, -45, -55, -99, -165, -495.
What is the Sum of all the Factors of 495?
Sum of all factors of 495 = (32 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (111 + 1 - 1)/(11 - 1) = 936
What are Prime Factors of 495?
The prime factors of 495 are 3, 5, 11.
What is the Greatest Common Factor of 495 and 354?
The factors of 495 and 354 are 1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, 495 and 1, 2, 3, 6, 59, 118, 177, 354 respectively.
Common factors of 495 and 354 are [1, 3].
Hence, the Greatest Common Factor of 495 and 354 is 3.
How Many Factors of 495 are also common to the Factors of 370?
Since, the factors of 495 are 1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, 495 and the factors of 370 are 1, 2, 5, 10, 37, 74, 185, 370.
Hence, [1, 5] are the common factors of 495 and 370.
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