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Factors of 35 are the list of integers that divide 35 exactly without leaving a remainder. 35 has a total of 4 factors which are 1, 5, 7, and 35. 35 itself is the biggest factor of 35 and 1 is the smallest factor of 35. On adding up all the factors, the sum of the factors of 35 is 48. The prime factorization of 35 is 5 × 7, where 5 and 7 are the two prime factors of 35. If two numbers when multiplied in pairs result in 35, then they are called the pair factor of 35. There are two pair factors of 35 which are (1, 35) and (5, 7). The factors of 35 can be integers but cannot be a decimal or fractions.
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Key Terms: Factors of 35, Prime Factors, Prime Factorization, Pair Factors, Composite Number, Remainder, Division, Factor Tree
What are the Factors of 35?
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The numbers that divide 35 completely and leave the remainder as zero are the factors of 35. The factors of 35 are all the numbers that are multiplied to get 35 as the product. 35 is a composite number which means that it has more than two factors. The factors of 35 are 1, 5, 7, and 35.
Factors of 35: 1, 5, 7, 35
Factors of 35
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| Chapter-Related Topics | ||
|---|---|---|
| Co Prime Numbers | Perfect Numbers | Properties of LCM and HCF |
| HCF | Multiplication and Division of Integers | Quotient |
Pair Factors of 35
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Pair factors of 35 refer to two numbers that when multiplied together give the number 35 as the output. There are both positive and negative pair factors of 35. The positive and negative pair factors of 35 are tabulated below.
Positive Pair Factors of 35
The positive pair factors of 35 are as follows:
| Positive Factors of 35 | Positive Pair Factors of 35 |
|---|---|
| 1 × 35 | (1, 35) |
| 5 × 7 | (5, 7) |
Negative Pair Factors of 35
The positive pair factors of 35 are as follows:
| Negative Factors of 35 | Negative Pair Factors of 35 |
|---|---|
| -1 × -35 | (-1, -35) |
| -5 × -7 | (-5, -7) |
Also Read: NCERT Solutions for Class 6 Maths Playing With Numbers
How to Find Factors of 35?
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Factors of 35 can easily be calculated by dividing 35 by a given number. If the number divides 35 completely, then it is a factor of 35, else not. The factors of 35 can be calculated with the help of two methods mainly which are as follows:
- Division Method
- Prime Factorization Method
Factors of 35 by Division Method
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The factors of 35 can be found with the help of the division method in which we divide 35 by different integers. If a number divides 35 completely and leaves the remainder zero, then the number is the factor of 35. We can divide 35 by various numbers starting from 1 and check whether that number is a factor of 35 or not.
- 35/1 = 35 (Factor = 1; Remainder = 0)
- 35/5 = 7 (Factor = 5; Remainder = 0)
- 35/7 = 5 (Factor = 7; Remainder = 0)
- 35/35 = 1 (Factor = 35; Remainder = 0)
If 35 is divided by any other number other than 1, 5, 7 and 35, it would leave a remainder which means that they are not the factors of 35. Thus, the factors of 35 are 1, 5, 7, and 35.
Read More: Factors of 72
Prime Factorization of 35
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Prime Factorization of 35 refers to the process of writing the number 35 as the product of its prime factors. Follow the given steps to perform the prime factorization of 35:
- Let us take a pair factor of 35, say (1, 35).
- 1 cannot be factored further a sit is neither a composite number nor a prime number. Now, we will take the other number 35, which is a composite number
- Now, we will split the composite number 35 into its prime factors.
- 35 can be written as the product of 5 and 7.
- Both 5 and 7 are the prime factors and they can not be factored further. Thus, 35 = 5 × 7
Prime Factorization of 35
Hence, the prime factorization of 35 is 5 × 7. The two prime factors of 35 are 5 and 7.
Factor Tree of 35
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The factors of 35 can also be represented in the form of a factor tree. The factor tree of 35 is as follows:
Factor Tree of 35
Read More: Relation Between HCF and LCM
Solved Examples on Factors of 35
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Example 1: What is the Least Common Multiple (LCM) and Greatest Common Divisor (GCD) of 35 and 53?
Solution: We will write down all the factors of 35 and 53 first,
- Factors of 35: 1, 5, 7, 35
- Factors of 53: 1, 53
Thus, the Least Common Multiple (LCM) of 35 and 53 is 1855. The Greatest Common Divisor (GCD) of 35 and 53 is 1.
Example 2: What are the common factors of 35 and 36?
Solution: Listing all the factors of 35 and 36,
- Factors of 35 = 1, 5, 7, 35
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.
Thus, there is only one common factor of 35 and 36 which is 1.
Read More:
| Related Topics | ||
|---|---|---|
| Prime Number Formula | Addition and Subtraction of Integers | Properties of Multiplication of Integers |
| LCM Formula | Real Numbers | Fundamental Theorem Of Arithmetic |
Things to Remember
- Factors of 35 are the numbers that divide 35 evenly with no remainder.
- The factors of 35 are 1, 5, 7, and 35.
- The prime factorization of 35 is 5 x 7.
- 5 and 7 are the two prime factors of 35.
- The sum of all the factors of 35 is 48.
- The pair factors of 35 are (1, 35) and (5, 7).
Sample Questions
Ques. Iqra has 35 pizza boxes. She wants to group the pizza box such that each stack gets equal pizza boxes. In how many ways can she do so? (3 Marks)
Ans. We know that Iqra has 35 pizzas. Using the concept of the factors of 35, she can group them in 4 ways.
- She can have a stack of 1 pizza box and 35 such groups.
- She can have a stack of 5 pizza boxes and 7 such groups.
- She can also have a stack of 7 pizza boxes and 5 such groups.
- Lastly, she can have a stack of 35 pizza boxes and only 1 group.
Hence, Iqra can stack the pizza boxes in 4 ways.
Ques. What are the common factors of 35 and 34? (2 Marks)
Ans. All the factors of 35 and 34 are as follows:
- Factors of 35 = 1, 5, 7, 35
- Factors of 34 = 1, 2, 17, 34
Thus, we can see that there is only one common factor of 35 and 34 which is 1.
Ques. Manushi wants to buy 35 books. However, she can buy only 5 books at once. Find out how many times she has to go to a book outlet to buy all the books. (3 Marks)
Ans. As Manushi can buy only 5 books at once, we need to find the number of times she has to go to the book outlet to buy all the books.
The pair factor of 5 which gives 35 as the product will be the number of times she has to go to the book store.
5 × _____ = 35.
Thus, Manushi will go 7 times to the book outlet to buy all the books.
Ques. List the common factors of 35 and 17. (2 Marks)
Ans. We will first mention all the factors of 35 and 17:
- Factors of 35: 1, 5, 7, and 35.
- Factors of 17: 1 and 17.
The common factor of 35 and 17 is 1 only. It implied that 35 and 17 are coprime numbers.
Ques. What is the total of all the factors of 35? (2 Marks)
Ans. We know that there are 4 factors of 35 which are 1, 5, 7, and 35. Adding up all these factors, we get
1 + 5 + 7 + 35 = 48
Thus, the sum of all the factors of 35 is 48.
Ques. List the common factors of 35 and 11. (2 Marks)
Ans. The factors of 35 and 11 are
- Factors of 35: 1, 5, 7, and 35.
- Factors of 11: 1, and 11.
35 and 11 have only one common factor which is 1.
Ques. Name the prime factors of 35. (1 Mark)
Ans. The prime factorization of 35 is 5 x 7 which means that the prime factors of 35 are 5 and 7.
Ques. Name the Greatest Common Factor of 35 and 33. (3 Marks)
Ans. The factors of 35 and 33 are as follows:
- Factors of 35 are 1, 5, 7, and 35.
- Factors of 33 are 1, 3, 11, and 33.
35 and 33 have only one common factor which is 1. It means that 35 and 33 are co-prime numbers. Thus, the Greatest Common Factor (GCF) of 35 and 33 is 1.
Ques. Check whether 7 is a factor of 35. (2 Marks)
Ans. In order to check whether 7 is a factor of 35, we will first divide 35 by it and check if the remainder is zero or not.
35 ÷ 7 = 5
As 7 divides 35 completely with zero remainder, hence 7 is a factor of 35.
Ques. List the positive and negative pair factors of 35. (2 Marks)
Ans. The positive and negative pair factors of 35 are as follows:
- Positive pair factors of 35: (1, 35) and (5, 7).
- Negative pair factors of 35: (-1, -35) and (-5, -7).
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