Factors of 484
Factors of 484 are numbers that, when multiplied in pairs give the product as 484. There are overall 9 factors of 484 i.e. 1, 2, 4, 11, 22, 44, 121, 242, 484 where 484 is the biggest factor. The Prime Factors and Pair Factors of 484 are 2 × 11 and (1, 484), (2, 242), (4, 121), (11, 44), (22, 22) respectively.
- All Factors of 484: 1, 2, 4, 11, 22, 44, 121, 242 and 484
- Negative Factors of 484: -1, -2, -4, -11, -22, -44, -121, -242 and -484
- Prime Factors of 484: 2, 11
- Prime Factorization of 484: 22 × 112
- Sum of Factors of 484: 931
1. | What Are the Factors of 484? |
2. | Factors of 484 by Prime Factorization |
3. | Factors of 484 in Pairs |
4. | FAQs on Factors of 484 |
What are Factors of 484?
Factors of 484 are pairs of those numbers whose products result in 484. These factors are either prime numbers or composite numbers.
How to Find the Factors of 484?
To find the factors of 484, we will have to find the list of numbers that would divide 484 without leaving any remainder.
- 484/4 = 121; therefore, 4 is a factor of 484 and 121 is also a factor of 484.
- 484/44 = 11; therefore, 44 is a factor of 484 and 11 is also a factor of 484.
☛ Also Check:
- Factors of 98 - The factors of 98 are 1, 2, 7, 14, 49, 98
- Factors of 96 - The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- Factors of 70 - The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
- Factors of 48 - The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 22 - The factors of 22 are 1, 2, 11, 22
Factors of 484 by Prime Factorization
- 484 ÷ 2 = 242
- 242 ÷ 2 = 121
Further dividing 121 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 121 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 484 can be written as 22 × 112 where 2, 11 are prime.
Factors of 484 in Pairs
Pair factors of 484 are the pairs of numbers that when multiplied give the product 484. The factors of 484 in pairs are:
- 1 × 484 = (1, 484)
- 2 × 242 = (2, 242)
- 4 × 121 = (4, 121)
- 11 × 44 = (11, 44)
- 22 × 22 = (22, 22)
Negative pair factors of 484 are:
- -1 × -484 = (-1, -484)
- -2 × -242 = (-2, -242)
- -4 × -121 = (-4, -121)
- -11 × -44 = (-11, -44)
- -22 × -22 = (-22, -22)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 484 Solved Examples
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Example 1: How many factors are there for 484?
Solution:
The factors of 484 are too many, therefore if we can find the prime factorization of 484, 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 484 = 22 × 112
Therefore, the total number of factors are (2 + 1) × (2 + 1) = 3 × 3 = 9 -
Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 484 and 215.
Solution:
The factors of 484 are 1, 2, 4, 11, 22, 44, 121, 242, 484 and factors of 215 are 1, 5, 43, 215.
Therefore, the Least Common Multiple of 484 and 215 is 104060 and Greatest Common Divisor (GCD) of 484 and 215 is 1. -
Example 3: Find if 4, 11, 44, 242 and 411 are factors of 484.
Solution:
When we divide 484 by 411 it leaves a remainder. Therefore, the number 411 is not a factor of 484. All numbers except 411 are factors of 484.
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Example 4: Find the product of all the prime factors of 484.
Solution:
Since, the prime factors of 484 are 2, 11. Therefore, the product of prime factors = 2 × 11 = 22.
FAQs on Factors of 484
What are the Factors of 484?
The factors of 484 are 1, 2, 4, 11, 22, 44, 121, 242, 484 and its negative factors are -1, -2, -4, -11, -22, -44, -121, -242, -484.
What is the Sum of all the Factors of 484?
Sum of all factors of 484 = (22 + 1 - 1)/(2 - 1) × (112 + 1 - 1)/(11 - 1) = 931
What are Prime Factors of 484?
The prime factors of 484 are 2, 11.
What is the Greatest Common Factor of 484 and 474?
The factors of 484 and 474 are 1, 2, 4, 11, 22, 44, 121, 242, 484 and 1, 2, 3, 6, 79, 158, 237, 474 respectively.
Common factors of 484 and 474 are [1, 2].
Hence, the Greatest Common Factor of 484 and 474 is 2.
How Many Factors of 312 are also common to the Factors of 484?
Since, the factors of 484 are 1, 2, 4, 11, 22, 44, 121, 242, 484 and the factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312.
Hence, [1, 2, 4] are the common factors of 484 and 312.
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