Factors of 3465 are numbers that, when multiplied in pairs give the product as 3465. There are overall 24 factors of 3465, of which 3, 5, 7, 11 are its prime factors. The sum of all factors of 3465 is 7488.
- All Factors of 3465: 1, 3, 5, 7, 9, 11, 15, 21, 33, 35, 45, 55, 63, 77, 99, 105, 165, 231, 315, 385, 495, 693, 1155 and 3465
- Prime Factors of 3465: 3, 5, 7, 11
- Prime Factorization of 3465: 32 × 51 × 71 × 111
- Sum of Factors of 3465: 7488
| 1. | What Are the Factors of 3465? |
| 2. | Factors of 3465 by Prime Factorization |
| 3. | Factors of 3465 in Pairs |
| 4. | FAQs on Factors of 3465 |
What are Factors of 3465?
Factors of 3465 are pairs of those numbers whose products result in 3465. These factors are either prime numbers or composite numbers.
How to Find the Factors of 3465?
To find the factors of 3465, we will have to find the list of numbers that would divide 3465 without leaving any remainder.
- 3465/385 = 9; therefore, 385 is a factor of 3465 and 9 is also a factor of 3465.
- 3465/105 = 33; therefore, 105 is a factor of 3465 and 33 is also a factor of 3465.
Similarly we can find other factors. Hence, the factors of 3465 are 1, 3, 5, 7, 9, 11, 15, 21, 33, 35, 45, 55, 63, 77, 99, 105, 165, 231, 315, 385, 495, 693, 1155, 3465.
☛ Also Check:
- Factors of 100 - The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
- Factors of 31 - The factors of 31 are 1, 31
- Factors of 26 - The factors of 26 are 1, 2, 13, 26
- Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- Factors of 81 - The factors of 81 are 1, 3, 9, 27, 81
Factors of 3465 by Prime Factorization
The number 3465 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 3465. The first step is to divide the number 3465 with the smallest prime factor, here it is 3. We keep dividing until it gives a non-zero remainder.
- 3465 ÷ 3 = 1155
- 1155 ÷ 3 = 385
Further dividing 385 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 385 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 3465 can be written as 32 × 51 × 71 × 111 where 3, 5, 7, 11 are prime.
Factors of 3465 in Pairs
Pair factors of 3465 are the pairs of numbers that when multiplied give the product 3465. The factors of 3465 in pairs are:
- 1 × 3465 = (1, 3465)
- 3 × 1155 = (3, 1155)
- 5 × 693 = (5, 693)
- 7 × 495 = (7, 495)
- 9 × 385 = (9, 385)
- 11 × 315 = (11, 315)
- 15 × 231 = (15, 231)
- 21 × 165 = (21, 165)
- 33 × 105 = (33, 105)
- 35 × 99 = (35, 99)
- 45 × 77 = (45, 77)
- 55 × 63 = (55, 63)
Negative pair factors of 3465 are:
- -1 × -3465 = (-1, -3465)
- -3 × -1155 = (-3, -1155)
- -5 × -693 = (-5, -693)
- -7 × -495 = (-7, -495)
- -9 × -385 = (-9, -385)
- -11 × -315 = (-11, -315)
- -15 × -231 = (-15, -231)
- -21 × -165 = (-21, -165)
- -33 × -105 = (-33, -105)
- -35 × -99 = (-35, -99)
- -45 × -77 = (-45, -77)
- -55 × -63 = (-55, -63)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 3465 Solved Examples
Example 1: How many factors are there for 3465?
Solution:
The factors of 3465 are too many, therefore if we can find the prime factorization of 3465, 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 3465 = 32 × 51 × 71 × 111
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 × 2 = 24Example 2: Find the LCM and Highest Common Factor (HCF) of 3465 and 2574.
Solution:
The factors of 3465 are 1, 3, 5, 7, 9, 11, 15, 21, 33, 35, 45, 55, 63, 77, 99, 105, 165, 231, 315, 385, 495, 693, 1155, 3465 and factors of 2574 are 1, 2, 3, 6, 9, 11, 13, 18, 22, 26, 33, 39, 66, 78, 99, 117, 143, 198, 234, 286, 429, 858, 1287, 2574.
Therefore, the LCM of 3465 and 2574 is 90090 and Highest Common Factor (HCF) of 3465 and 2574 is 99.
Example 3: Find if 9, 15, 35, 45, 55, 315, 495 and 3132 are factors of 3465.
Solution:
When we divide 3465 by 3132 it leaves a remainder. Therefore, the number 3132 is not a factor of 3465. All numbers except 3132 are factors of 3465.
Example 4: Find the product of all the prime factors of 3465.
Solution:
Since, the prime factors of 3465 are 3, 5, 7, 11. Therefore, the product of prime factors = 3 × 5 × 7 × 11 = 1155.
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FAQs on Factors of 3465
What are the Factors of 3465?
The factors of 3465 are 1, 3, 5, 7, 9, 11, 15, 21, 33, 35, 45, 55, 63, 77, 99, 105, 165, 231, 315, 385, 495, 693, 1155, 3465 and its negative factors are -1, -3, -5, -7, -9, -11, -15, -21, -33, -35, -45, -55, -63, -77, -99, -105, -165, -231, -315, -385, -495, -693, -1155, -3465.
What is the Sum of all the Factors of 3465?
Sum of all factors of 3465 = (32 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (71 + 1 - 1)/(7 - 1) × (111 + 1 - 1)/(11 - 1) = 7488
What are the Prime Factors of 3465?
The prime factors of 3465 are 3, 5, 7, 11.
What is the Greatest Common Factor of 3465 and 642?
The factors of 3465 and 642 are 1, 3, 5, 7, 9, 11, 15, 21, 33, 35, 45, 55, 63, 77, 99, 105, 165, 231, 315, 385, 495, 693, 1155, 3465 and 1, 2, 3, 6, 107, 214, 321, 642 respectively.
Common factors of 3465 and 642 are [1, 3].
Hence, the Greatest Common Factor (GCF) of 3465 and 642 is 3.
How Many Factors of 3465 are also Factors of 1542?
Since, the factors of 3465 are 1, 3, 5, 7, 9, 11, 15, 21, 33, 35, 45, 55, 63, 77, 99, 105, 165, 231, 315, 385, 495, 693, 1155, 3465 and the factors of 1542 are 1, 2, 3, 6, 257, 514, 771, 1542.
Hence, [1, 3] are the common factors of 3465 and 1542.
