The number 35 is composite, meaning it has factors other than 1 and itself. The factors of 35 are 1, 5, 7, and 35. When we say that a number is a factor of 35, it means it evenly divides 35 without leaving a remainder. For example, 5 is a factor of 35 because 35 divided by 5 equals 7.
Similarly, 7 is a factor of 35 because 35 divided by 7 also equals 5. The Factors of number 35 play a significant role in various mathematical operations, such as finding common multiples or factors of other numbers.
Understanding the Factors of number 35 is useful in many real-life scenarios. For instance, if you have 35 identical items and want to distribute them equally among a group of people, knowing the factors helps determine the number of people you can divide them among without any leftovers.
Moreover, the Factors of the number 35 are essential in determining whether 35 is a prime number. Since 35 has factors other than 1 and itself, it is not a prime number but a composite number. Factors provide valuable insights into the properties and relationships of numbers, aiding in mathematical computations and problem-solving.
What are the Factors of 35?
There are four factors in all, with 35 being the largest. The positive aspects that affect 35 are 1, 5, 7, and 35.
- Factors: 1, 5, 7 and 35
- Negative Factors: -1, -5, -7 and -35
- Prime Factors: 5, 7
- Prime Factorization: 5 × 7 = 5 × 7
- Sum of Factors: 48
Key Points:
- The numbers that divide 35 evenly and leave no remainder are known as Factors of number 35.
- 1, 5, 7, and 35 belong to the number 35.
- 5 x 7 is the prime factorization of 35.
- The two main multiples s of 35 are 5 and 7.
- 48 is the sum of all 35 factors.
- 35 has the pair components (1, 35) and (5, 7).
Pair Factors of 35
The pair of numbers is called the pair factor of 35 if two numbers are multiplied to get the number 35. As mentioned before, we have 35 pair factors that are both positive and negative. Below are 35’s positive and negative pair factors:
Positive Pair Factors of 35:
| Positive Factors | Positive Pair Factors |
| 1 × 35 | (1, 35) |
| 5 × 7 | (5, 7) |
Negative Pair Factors of 35:
| Negative Factors | Negative Pair Factors |
| -1 × -35 | (-1, -35) |
| -5 × -7 | (-5, -7) |
How to Find Factors of 35?
There are two ways to find the factors of the number 35, and they are as follows:
- Division method
- Prime factorization method
Factors of 35 by Division Method
By dividing 35 by various integers, the division method can be used to determine the Factors of the number 35. The integers are the Factors of the number 35 if they divide 35 and leave a remainder of 0. Let’s begin by dividing 35 by 1, then go on to other integers.
| Division | Factor | Remainder |
| 35 ÷ 1 | 1 | 0 |
| 35÷ 2 | 5 | 0 |
| 35÷ 3 | 7 | 0 |
| 35 ÷ 6 | 35 | 0 |
Prime Factorization of 35:
To find the prime factorization of 35, we can use a method called prime factorization by division. Here’s how you can do it:
- Start with the number 35.
- Find the smallest prime number that divides evenly into 35. In this case, it is 5.
- Divide 35 by 5, which gives you 7.
- Now, 7 is a prime number, so the prime factorization 35 is 5 multiplied by 7 (5 x 7).
- Therefore, the prime factorization of 35 is 5 x 7.
Factor Tree of 35:
To find the factor tree of 35, you can follow these steps:
- Start by writing down the number 35.
- Think of two Factors of the number 35 that multiply together to give 35. In this case, 5 and 7 are prime Factors of number 35.
- Continue breaking down any composite factors into their prime factors. Since both 5 and 7 are already prime, we can stop here.
- The factor tree is complete, and the prime Factors of number 35 are 5 and 7.
This is how the factor tree of 35 would look like:
So, the factor tree of 35 is represented by the branches 5 and 7 stemming from the number 35.
Example 1:
Find the common factors of 34 and 35.
Solution:
To find the common factors of 34 and 35, we can list the factors of each number and identify the ones they have in common.
The Factors of number 35 are 1, 5, 7, and 35.
The factors of 34 are 1, 2, 17, and 34.
Example 2:
What is the Least Common Multiple (LCM) of 35 and 85?
Solution:
The LCM of 35 and 85 is 595, and the GCD is 5.
Example 3:
Find the sum of all factors of 35 and divide it by the sum of even factors of 48.
Solution:
To find the sum of all Factors of number 35, we can list its factors and add them up:
The Factors of number 35 are 1, 5, 7, and 35.
Sum of factors = 1 + 5 + 7 + 35 = 48.
To find the sum of even factors of 48, we list its factors and select the even ones:
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
Even factors = 2 + 4 + 6 + 8 + 12 + 16 + 24 + 48 = 120.
Now, we can divide the sum of Factors of number 35 by the sum of even factors of 48:
48 / 120 = 0.4.
Therefore, the result is 0.4.
Yes! It is
Factors of number 35 are 1, 5, 7, 35, and the sum of all these factors is 1 + 5 + 7 + 35 = 48
