Factors of 3630
Factors of 3630 are the list of integers that we can split evenly into 3630. There are overall 24 factors of 3630 among which 3630 is the biggest factor and its prime factors are 2, 3, 5, 11. The sum of all factors of 3630 is 9576.
- All Factors of 3630: 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 121, 165, 242, 330, 363, 605, 726, 1210, 1815 and 3630
- Prime Factors of 3630: 2, 3, 5, 11
- Prime Factorization of 3630: 21 × 31 × 51 × 112
- Sum of Factors of 3630: 9576
1. | What Are the Factors of 3630? |
2. | Factors of 3630 by Prime Factorization |
3. | Factors of 3630 in Pairs |
4. | FAQs on Factors of 3630 |
What are Factors of 3630?
Factors of 3630 are pairs of those numbers whose products result in 3630. These factors are either prime numbers or composite numbers.
How to Find the Factors of 3630?
To find the factors of 3630, we will have to find the list of numbers that would divide 3630 without leaving any remainder.
- 3630/5 = 726; therefore, 5 is a factor of 3630 and 726 is also a factor of 3630.
- 3630/10 = 363; therefore, 10 is a factor of 3630 and 363 is also a factor of 3630.
☛ Also Check:
- Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- Factors of 20 - The factors of 20 are 1, 2, 4, 5, 10, 20
- Factors of 108 - The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
- Factors of 56 - The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
- Factors of 51 - The factors of 51 are 1, 3, 17, 51
Factors of 3630 by Prime Factorization
- 3630 ÷ 2 = 1815
Further dividing 1815 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 1815 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 3630 can be written as 21 × 31 × 51 × 112 where 2, 3, 5, 11 are prime.
Factors of 3630 in Pairs
Pair factors of 3630 are the pairs of numbers that when multiplied give the product 3630. The factors of 3630 in pairs are:
- 1 × 3630 = (1, 3630)
- 2 × 1815 = (2, 1815)
- 3 × 1210 = (3, 1210)
- 5 × 726 = (5, 726)
- 6 × 605 = (6, 605)
- 10 × 363 = (10, 363)
- 11 × 330 = (11, 330)
- 15 × 242 = (15, 242)
- 22 × 165 = (22, 165)
- 30 × 121 = (30, 121)
- 33 × 110 = (33, 110)
- 55 × 66 = (55, 66)
Negative pair factors of 3630 are:
- -1 × -3630 = (-1, -3630)
- -2 × -1815 = (-2, -1815)
- -3 × -1210 = (-3, -1210)
- -5 × -726 = (-5, -726)
- -6 × -605 = (-6, -605)
- -10 × -363 = (-10, -363)
- -11 × -330 = (-11, -330)
- -15 × -242 = (-15, -242)
- -22 × -165 = (-22, -165)
- -30 × -121 = (-30, -121)
- -33 × -110 = (-33, -110)
- -55 × -66 = (-55, -66)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 3630 Solved Examples
-
Example 1: How many factors are there for 3630?
Solution:
The factors of 3630 are too many, therefore if we can find the prime factorization of 3630, 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 3630 = 21 × 31 × 51 × 112
Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (2 + 1) = 2 × 2 × 2 × 3 = 24 -
Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 3630 and 1106.
Solution:
The factors of 3630 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 121, 165, 242, 330, 363, 605, 726, 1210, 1815, 3630 and factors of 1106 are 1, 2, 7, 14, 79, 158, 553, 1106.
Therefore, the Least Common Multiple of 3630 and 1106 is 2007390 and Greatest Common Divisor (GCD) of 3630 and 1106 is 2. -
Example 3: Find if 3, 11, 15, 110, 363, 605, 636 and 726 are factors of 3630.
Solution:
When we divide 3630 by 636 it leaves a remainder. Therefore, the number 636 is not a factor of 3630. All numbers except 636 are factors of 3630.
-
Example 4: Find the product of all the prime factors of 3630.
Solution:
Since, the prime factors of 3630 are 2, 3, 5, 11. Therefore, the product of prime factors = 2 × 3 × 5 × 11 = 330.
FAQs on Factors of 3630
What are the Factors of 3630?
The factors of 3630 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 121, 165, 242, 330, 363, 605, 726, 1210, 1815, 3630 and its negative factors are -1, -2, -3, -5, -6, -10, -11, -15, -22, -30, -33, -55, -66, -110, -121, -165, -242, -330, -363, -605, -726, -1210, -1815, -3630.
What is the Sum of all the Factors of 3630?
Sum of all factors of 3630 = (21 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) × (112 + 1 - 1)/(11 - 1) = 9576
What numbers are the Pair Factors of 3630?
The pair factors of 3630 are (1, 3630), (2, 1815), (3, 1210), (5, 726), (6, 605), (10, 363), (11, 330), (15, 242), (22, 165), (30, 121), (33, 110), (55, 66).
What is the Greatest Common Factor of 3630 and 189?
The factors of 3630 and 189 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 121, 165, 242, 330, 363, 605, 726, 1210, 1815, 3630 and 1, 3, 7, 9, 21, 27, 63, 189 respectively.
Common factors of 3630 and 189 are [1, 3].
Hence, the Greatest Common Factor (GCF) of 3630 and 189 is 3.
How Many Factors of 3630 are also common to the Factors of 1836?
Since, the factors of 3630 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 121, 165, 242, 330, 363, 605, 726, 1210, 1815, 3630 and the factors of 1836 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 27, 34, 36, 51, 54, 68, 102, 108, 153, 204, 306, 459, 612, 918, 1836.
Hence, [1, 2, 3, 6] are the common factors of 3630 and 1836.
visual curriculum