Factors of 567
Factors of 567 are the list of integers that we can split evenly into 567. It has total 10 factors of which 567 is the biggest factor and the prime factors of 567 are 3, 7. The sum of all factors of 567 is 968.
- All Factors of 567: 1, 3, 7, 9, 21, 27, 63, 81, 189 and 567
- Negative Factors of 567: -1, -3, -7, -9, -21, -27, -63, -81, -189 and -567
- Prime Factors of 567: 3, 7
- Prime Factorization of 567: 34 × 71
- Sum of Factors of 567: 968
1. | What Are the Factors of 567? |
2. | Factors of 567 by Prime Factorization |
3. | Factors of 567 in Pairs |
4. | FAQs on Factors of 567 |
What are Factors of 567?
Factors of 567 are pairs of those numbers whose products result in 567. These factors are either prime numbers or composite numbers.
How to Find the Factors of 567?
To find the factors of 567, we will have to find the list of numbers that would divide 567 without leaving any remainder.
- 567/27 = 21; therefore, 27 is a factor of 567 and 21 is also a factor of 567.
- 567/63 = 9; therefore, 63 is a factor of 567 and 9 is also a factor of 567.
☛ Also Check:
- Factors of 42 - The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 29 - The factors of 29 are 1, 29
- Factors of 7 - The factors of 7 are 1, 7
- Factors of 100 - The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
- Factors of 49 - The factors of 49 are 1, 7, 49
Factors of 567 by Prime Factorization
- 567 ÷ 3 = 189
- 189 ÷ 3 = 63
- 63 ÷ 3 = 21
- 21 ÷ 3 = 7
Further dividing 7 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 7 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 567 can be written as 34 × 71 where 3, 7 are prime.
Factors of 567 in Pairs
Pair factors of 567 are the pairs of numbers that when multiplied give the product 567. The factors of 567 in pairs are:
- 1 × 567 = (1, 567)
- 3 × 189 = (3, 189)
- 7 × 81 = (7, 81)
- 9 × 63 = (9, 63)
- 21 × 27 = (21, 27)
Negative pair factors of 567 are:
- -1 × -567 = (-1, -567)
- -3 × -189 = (-3, -189)
- -7 × -81 = (-7, -81)
- -9 × -63 = (-9, -63)
- -21 × -27 = (-21, -27)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 567 Solved Examples
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Example 1: How many factors are there for 567?
Solution:
The factors of 567 are too many, therefore if we can find the prime factorization of 567, 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 567 = 34 × 71
Therefore, the total number of factors are (4 + 1) × (1 + 1) = 5 × 2 = 10 -
Example 2: Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of 567 and 345.
Solution:
The factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567 and factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345.
Therefore, the Least Common Multiple (LCM) of 567 and 345 is 65205 and Greatest Common Factor (GCF) of 567 and 345 is 3. -
Example 3: Find if 1, 9, 27, 63, 345 and 567 are factors of 567.
Solution:
When we divide 567 by 345 it leaves a remainder. Therefore, the number 345 is not a factor of 567. All numbers except 345 are factors of 567.
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Example 4: Find the product of all the prime factors of 567.
Solution:
Since, the prime factors of 567 are 3, 7. Therefore, the product of prime factors = 3 × 7 = 21.
FAQs on Factors of 567
What are the Factors of 567?
The factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567 and its negative factors are -1, -3, -7, -9, -21, -27, -63, -81, -189, -567.
What is the Sum of all the Factors of 567?
Sum of all factors of 567 = (34 + 1 - 1)/(3 - 1) × (71 + 1 - 1)/(7 - 1) = 968
What are Prime Factors of 567?
The prime factors of 567 are 3, 7.
What is the Greatest Common Factor of 567 and 564?
The factors of 567 and 564 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567 and 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564 respectively.
Common factors of 567 and 564 are [1, 3].
Hence, the Greatest Common Factor (GCF) of 567 and 564 is 3.
How Many Factors of 567 are also Factors of 215?
Since, the factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567 and factors of 215 are 1, 5, 43, 215. Hence, 567 and 215 have only one common factor which is 1. Therefore, 567 and 215 are co-prime.
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