What are the Factors of 35?
If the number 35 is divided by a positive integer such that the remainder is zero, the integer is known as a factor of 35. Here, the quotient obtained on division is also a factor of 35.
The factors of 35 are 1, 5, 7, and 35 because all these numbers divide the number 35 evenly.
List of the Factors of 35
Divisibility rules and division facts can be used to determine the factors of 35.
Divisor | Is the number a factor of 35? | Multiplication equation |
|---|---|---|
1 | Yes, 1 is a factor of every number. | 1 \( \times \) 35 = 35 |
2 | No, 35 is not even. | - |
3 | No, 3 + 5 = 8 is not divisible by 3. | - |
4 | No, 35 \( \div \) 4 = 8 R3 | - |
5 | Yes, ones digit is 0 or 5. | 5 \( \times \) 7 = 35 |
6 | No, 35 is not even. | - |
7 | Yes, 35 \( \div \) 7 = 5 R0 | 7 \( \times \) 5 = 35 |
8 | No, 35 \( \div \) 8 = 4 R3 | - |
9 | No, 35 \( \div \) 9 = 3 R8 | - |
So, the factors of 35 are 1, 5, 7, and 35.
The Factors of 35 by the Division method
We can check whether a number is a factor of 35 by dividing 35 by that number. If the remainder obtained is zero, the number is a factor, otherwise not.
- If we divide 35 by 1, we get the quotient and the remainder as 35 and 0, respectively. So, 1 is a factor of 35.
- If we divide 35 by 5, we get the quotient and the remainder as 7 and 0, respectively. So, 5 is a factor of 35.
- If we divide 35 by 7, we get the quotient and remainder as 5 and 0, respectively. So, 7 is a factor of 35.
- If we divide 35 by 35, we get the quotient and remainder as 1 and 0, respectively. So, 35 is a factor of 35.
[Note: If we divide 35 by 6, we get the quotient and remainder as 5 and 5, respectively. So, 6 is not a factor of 35. Similarly, you can check for other numbers as well.]
The Prime Factorization of 35
If a natural number can be expressed as a product of prime numbers, 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.
The prime factorization of 35 can be represented by using a factor tree as shown below.
So, the prime factorization of 35 is 35 = 5 \( \times \) 7, and the prime factors of 35 are 5 and 7.
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Factor pairs of 35
A factor pair of a number is a set of any of its two factors such that their product is the number itself. A factor pair can be negative or positive.
The factor pairs of 35 are (1,35) and (5,7).
1 \( \times \) 35 = 35
5 \( \times \) 7 = 35
Positive Factor pairs of 35
Positive Factors of 35 | Positive Factor Pairs of 35 |
|---|---|
1 \( \times \) 35 | (1, 35) |
5 \( \times \) 7 | (7, 5) |
Solved Factors of 35 Examples
Example 1: Find the common factors of 28 and 35.
Solution:
Factors of 28 = 1, 2, 4, 7, 14, and 28
Factors of 35 = 1, 5, 7, and 35
Therefore, the common factors of 28 and 35 are 1 and 7.
Example 2: Find the greatest common factor of 35 and 90.
Solution:
Factors of 35 = 1, 5, 7, and 35
Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90
So, the common factors of 35 and 90 are 1 and 5.
Therefore, the greatest common factor of 35 and 90 is 5.
Example 3: Andrew wants to hang a rectangular photo frame in his room. The area available on the wall for hanging the frame is 35 cm\( ^2 \). Find the possible dimensions of the rectangular frame.
Solution:
The area of the rectangular frame is the area available on the wall, that is, 35 cm\( ^2 \).
Area of frame = length x width
35 = length x width
So, the dimensions of the frame will be the factor pairs of 35, which are, (1,35), (5,7), (7,5), and (35,1)
Therefore, the possible dimensions of the rectangular frame are:
Length in centimeters | Breadth in centimeters |
|---|---|
1 | 35 |
5 | 7 |
7 | 5 |
35 | 1 |
The factors of 35 are the numbers that divide 35 exactly, leaving the remainder as zero. The number 35 is exactly divisible by 1, 5, 7, and 35 only. So, the factors of 35 are 1, 5, 7, and 35.
The division of any positive number by 1 results in zero as the remainder, and the quotient is the number itself. Hence, 1 is a factor of all positive numbers.
The factors of 35 are 1, 5, 7, and 35. Here, 5 and 7 are prime numbers. So, 5 and 7 are the prime factors of 35.
Composite numbers are those numbers which have a factor other than 1 and themselves, that is, a composite number has more than two factors.
8 is not a factor of 35 because when we divide 35 by 8, the remainder is 3, that is, not zero.