Factors of 1220
Factors of 1220 are the list of integers that we can split evenly into 1220. It has total 12 factors of which 1220 is the biggest factor and the prime factors of 1220 are 2, 5, 61. The sum of all factors of 1220 is 2604.
- All Factors of 1220: 1, 2, 4, 5, 10, 20, 61, 122, 244, 305, 610 and 1220
- Prime Factors of 1220: 2, 5, 61
- Prime Factorization of 1220: 22 × 51 × 611
- Sum of Factors of 1220: 2604
1. | What Are the Factors of 1220? |
2. | Factors of 1220 by Prime Factorization |
3. | Factors of 1220 in Pairs |
4. | FAQs on Factors of 1220 |
What are Factors of 1220?
Factors of 1220 are pairs of those numbers whose products result in 1220. These factors are either prime numbers or composite numbers.
How to Find the Factors of 1220?
To find the factors of 1220, we will have to find the list of numbers that would divide 1220 without leaving any remainder.
- 1220/61 = 20; therefore, 61 is a factor of 1220 and 20 is also a factor of 1220.
- 1220/122 = 10; therefore, 122 is a factor of 1220 and 10 is also a factor of 1220.
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- Factors of 48 - The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 56 - The factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56
- Factors of 54 - The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
Factors of 1220 by Prime Factorization
- 1220 ÷ 2 = 610
- 610 ÷ 2 = 305
Further dividing 305 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 305 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 1220 can be written as 22 × 51 × 611 where 2, 5, 61 are prime.
Factors of 1220 in Pairs
Pair factors of 1220 are the pairs of numbers that when multiplied give the product 1220. The factors of 1220 in pairs are:
- 1 × 1220 = (1, 1220)
- 2 × 610 = (2, 610)
- 4 × 305 = (4, 305)
- 5 × 244 = (5, 244)
- 10 × 122 = (10, 122)
- 20 × 61 = (20, 61)
Negative pair factors of 1220 are:
- -1 × -1220 = (-1, -1220)
- -2 × -610 = (-2, -610)
- -4 × -305 = (-4, -305)
- -5 × -244 = (-5, -244)
- -10 × -122 = (-10, -122)
- -20 × -61 = (-20, -61)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 1220 Solved Examples
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Example 1: How many factors are there for 1220?
Solution:
The factors of 1220 are too many, therefore if we can find the prime factorization of 1220, 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 1220 = 22 × 51 × 611
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12 -
Example 2: Find the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 1220 and 310.
Solution:
The factors of 1220 are 1, 2, 4, 5, 10, 20, 61, 122, 244, 305, 610, 1220 and factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310.
Therefore, the Least Common Multiple (LCM) of 1220 and 310 is 37820 and Greatest Common Divisor (GCD) of 1220 and 310 is 10. -
Example 3: Find if 4, 10, 20, 305, 521, 610 and 1220 are factors of 1220.
Solution:
When we divide 1220 by 521 it leaves a remainder. Therefore, the number 521 is not a factor of 1220. All numbers except 521 are factors of 1220.
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Example 4: Find the product of all the prime factors of 1220.
Solution:
Since, the prime factors of 1220 are 2, 5, 61. Therefore, the product of prime factors = 2 × 5 × 61 = 610.
FAQs on Factors of 1220
What are the Factors of 1220?
The factors of 1220 are 1, 2, 4, 5, 10, 20, 61, 122, 244, 305, 610, 1220 and its negative factors are -1, -2, -4, -5, -10, -20, -61, -122, -244, -305, -610, -1220.
What is the Sum of all the Factors of 1220?
Sum of all factors of 1220 = (22 + 1 - 1)/(2 - 1) × (51 + 1 - 1)/(5 - 1) × (611 + 1 - 1)/(61 - 1) = 2604
What Numbers are the Prime Factors of 1220?
The prime factors of 1220 are 2, 5, 61.
What is the Greatest Common Factor of 1220 and 835?
The factors of 1220 and 835 are 1, 2, 4, 5, 10, 20, 61, 122, 244, 305, 610, 1220 and 1, 5, 167, 835 respectively.
Common factors of 1220 and 835 are [1, 5].
Hence, the Greatest Common Factor (GCF) of 1220 and 835 is 5.
How Many Factors of 449 are also common to the Factors of 1220?
Since, the factors of 1220 are 1, 2, 4, 5, 10, 20, 61, 122, 244, 305, 610, 1220 and factors of 449 are 1, 449. Hence, 1220 and 449 have only one common factor which is 1. Therefore, 1220 and 449 are co-prime.
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