Factors of 529 Using Prime Factorization
Factors of 529
The factors of 529 are those numbers that divide the number 529 exactly and as seen earlier, leave no remainder. We will learn how we can find the list of factors, prime factors and factor pairs of 529.
Factors | Factor Pairs | Prime Factorization |
|---|---|---|
1, 23 and 529 | (23, 23) and (1, 529) | 23 x 23 |
List of Factors of 529
By applying divisibility rules and division facts, we can obtain the list of factors for 529.
Divisor | Is the number a factor of 529? | Multiplication Equation |
|---|---|---|
1 | Yes, 1 is a factor of every number | 1 x 529 = 529 |
2 | No, 529 is odd | - |
3 | No, 5 + 2 + 9 = 16 is not divisible by 3 | - |
4 | No, 529 ÷ 4 = 132 R1 | - |
5 | No, the ones digit is not 0 or 5 | - |
6 | No, 529 ÷ 6 = 88 R1 | - |
7 | No, 529 ÷ 7 = 75 R4 | - |
8 | No, 529 ÷ 8 = 66 R1 | - |
This list continues till 23, and beyond that we can stop listing the factors.
Hence, the three factors of 529 are 1, 23, and 529.
Prime Factors of 529
A natural number can be also obtained by multiplying some prime numbers. In this case, these prime numbers are known as the prime factors of that natural number. The process of writing this multiplication of prime factors is known as prime factorization.
Since 529 is a composite number having multiple factors, we can divide those factors to get prime factors. We can divide 529 by a natural number less than itself to write out the flow of the prime factorization. The prime factorization of 529 can be represented using a factor tree as follows:
Therefore, 23 is the prime factor of the number 529.
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Rapid Recall
Factors of 529 are,
Solved Factors of 529 Examples
Example 1: Find the common factors of 18 and 529.
Solution:
Factors of 18 = 1, 2, 3, 6, 9, and 18.
Factors of 529 = 1, 23, and 529.
Therefore, the common factor of 18 and 529 is 1.
Example 2: Find the common factors of 74 and 529.
Solution:
Factors of 74 = 1, 2, 37 and 74.
Factors of 529 = 1, 23 and 529.
Therefore, the common factor of 74 and 529 is 1.
Example 3: Find the common factors of 37 and 529.
Solution:
Factors of 37 = 1 and 37.
Factors of 529 = 1, 23, and 529.
Therefore, the common factor of 37 and 529 is 1.
The factors of 529 are 1, 23, and 529.
So, the least factor of 529 is 1, and the greatest factor is 529 itself.
The factors of 529 are 1, 23, and 529.
Sum of the factors = 1 + 23 + 529 = 553
So, the sum of the factors of 529 is 553.
No, 55 is not a factor of 529. This is because when the number 55 divides 529, the quotient is 9 and the remainder as 34.
The prime factorization of 529 is 23 times 23.
The factor pairs of 529 are (1, 529) and (23, 23).
Composite numbers are those numbers which have a factor other than 1 or itself. For example 14, 15, 16 and so on are composite numbers.
The factors of 529 are 1, 23 and 529.
So, the smallest factor of 529 is 1, and the greatest factor is 529 itself.