Education Content Expert
Factors of 49 are the numbers that can be divided uniformly into 49. 49 is a composite number, thus, it has more than two factors. There are three factors of 49 which are 1, 7, and 49 itself. Pair factors of 49 are the numbers that when multiplied together result in the original number 49. (1, 49) and (7, 7) are the two pair factors of 49. The prime factorization of 49 is 7 × 7 = 72. Thus, 7 is the only prime factor of 49. The sum of the factors of 49 is 57.
Read More: NCERT Solutions for Class 6 Maths Playing With Numbers
| Table of Content |
Key Terms: Factors of 49, Prime Factorization, Remainder, Composite Number, Integers, Prime Factors, Pair Factors, Division
What are Factors of 49?
[Click Here for Sample Questions]
Factors of 49 are the natural numbers that can divide the number 49 evenly or into equal parts. In other words, when two numbers are multiplied to get the original number 49, those numbers are referred to as the factors of 49. The number 49 has three factors in total which are 1, 7, and 49.
Factors of 49
Read More:
| Relevant Concepts | ||
|---|---|---|
| Factors of 25 | Factors of 12 | Factors of 48 |
| Factors of 16 | Factors of 18 | Factors of 24 |
| Factors of 15 | Factors of 28 | Factors of 72 |
| Factors of 42 | Factors of 50 | Factors of 32 |
How to Calculate Factors of 49?
[Click Here for Sample Questions]
Factors of 49 can be calculated through the division method. Divide the number 49 by any number and check if it divides 49 completely, leaving no remainder.
- 49 ÷ 1 = 49
- 49 ÷ 7 = 7
- 49 ÷ 49 = 1
Thus, we can see that 1, 7, and 49 divide the number 49 completely leaving no remainder. Thus, the factors of 49 are 1, 7, and 49.
Prime Factorization of 49
[Click Here for Sample Questions]
Prime Factorization of 49 refers to the process of expressing 49 as a product of its prime factors. The prime factorization of 49 can be done with the help of the given steps:
Step 1: 49 can be divided evenly by 7. Thus, 7 is the smallest prime number that divides 49.
49 ÷ 7 = 7
Step 2: 7 is a prime number by itself. It can therefore be divided by either 1 or by itself.
7 ÷ 7 = 1
Here, we have received 1 at the end, so further division is not possible. Thus, the prime factorization of 49 is 7 x 7 or 72 with 7 as the only prime factor of 49.
Prime Factorization of 49
Read More: Prime Number Formula
Factor Tree of 49
[Click Here for Sample Questions]
Factors of 49 can be split into prime factors by the method of prime factorization. Thus. the factor tree of 49 is as follows:
Factor Tree of 49
Factors of 49 in Pairs
[Click Here for Sample Questions]
The numbers that give the original number 49 on multiplication with each other are known as pair factors of 49.
- 1 × 49 = 49
- 7 × 7 = 49
Therefore, (1, 49) and (7, 7) are the positive pair factors of 49.
Now, if we take into account the negative pair factors;
- -1 × -49 = 49
- -7 × -7 = 49
Therefore, (-1, -49) and (-7, -7) are the negative pair factors of 49.
Read More: Twin Primes
Solved Examples on Factors of 49
[Click Here for Sample Questions]
Example 1: Find the GCF of 49 and 84.
Solution: We will first write down all the factors of 49 and 84.
- Factors of 49 = 1, 7, 49
- Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
There are only two common factors of 49 and 84 which are 1 and 7. Thus, 7 is the GCF of 49 and 84.
GCF (49, 84) = 7
Example 2: What are the common factors of 40 and 49?
Solution: Listing all the factors of 40 and 49, we get
- Factors of 49 = 1, 7, 49
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
Thus, 49 and 40 have only one common factor which is 1 which means that they are co-prime numbers.
Also Check:
| Related Topics | ||
|---|---|---|
| Greatest Common Divisor | Quotient | Relation Between HCF and LCM |
| Properties of LCM and HCF | Dividend | HCF |
Things to Remember
- Factors of 49 are the numbers that divide 49 completely leaving zero as the remainder.
- Factors of 49 are 1, 7, and 49.
- The sum of all the factors of 49 is 57.
- The prime factorization of 49 is 7 × 7.
- There is only one prime factor of 49 which is 7.
- The pair factors of 49 are (1, 49), and (7, 7).
Sample Questions
Ques. What are the factors of 49? (2 Marks)
Ans. Factors of 49 are the numbers that divide 49 completely leaving zero as the remainder at the end of the division process. 49 has only three factors which are 1, 7, and 49 itself.
Ques. Is 49 a composite or prime number? (2 Marks)
Ans. A prime number is one that can only be divided by itself and 1. A composite number is one that is divisible by more than 2 factors. Thus, 49 is a composite number because it has more than two factors. There are a total of 3 factors of 49 which are 1, 7, and 49.
Ques. Is 49 a Perfect square? (2 Marks)
Ans. A perfect square is defined as a number that can be expressed as the product of two equal integers. 49 is a perfect square because it gives out a whole number on squaring.
√49 = 7 x 7 = 7
The square root of 49 is 7 which is a whole number. Thus, 49 is a perfect square.
Ques. How is 49 expressed as the product of prime factors? (2 Marks)
Ans. Prime factorization is the process of expressing a number as the product of its prime factors. Thus, 49 is expressed as a product of prime factors in the following manner:
49 = 7 x 7 = 72
Ques. What are the multiples of 49? (2 Marks)
Ans. The multiples of 49 are the numbers obtained when 49 is multiplied by an integer. The first 10 multiples of 49 are as follows:
- 49 × 1 = 49
- 49 × 2 = 98
- 49 × 3 = 147
- 49 × 4 = 196
- 49 × 5 = 245
- 49 × 6 = 294
- 49 × 7 = 343
- 49 × 8 = 392
- 49 × 9 = 441
- 49 × 10 = 490
Ques. What is the price of each rose if seven roses are purchased for Rs. 49? (2 Marks)
Ans. It is given that seven flowers were bought in total.
- Cost of Seven Roses = Rs. 49
- Cost of Each Rose = 49/7 = 7
Thus, the cost of each rose is Rs. 7.
Ques. What is the sum of all the factors of 49? Find their mean. (2 Marks)
Ans. 1, 7, and 49 are the factors of 49.
Sum of Factors of 49 = 1 + 7 + 49 = 57
To calculate the average, we need to divide the sum by the total number of factors.
57/3 = 19
Ques. List the common factors of 45 and 49. (2 Marks)
Ans. We will first list all the factors of both numbers
- Factors of 49: 1, 7, 49
- Factors of 45: 1, 3, 5, 9, 15, 45
Thus, there is only one common factor between 45 and 49 which is 1.
Ques. What are the positive and negative pair factors of 49? (2 Marks)
Ans. The positive and negative pair factors of 49 are as follows:
- Positive Pair Factors of 49: (1, 49), and (7, 7).
- Negative Pair Factors of 49 (-1, -49), and (-7, -7).
Ques. Is 3 a factor of 49? (2 Marks)
Ans. To check whether 3 is a factor of 49 or not, we will divide 49 by 3,
49 ÷ 3 = 16.33
We can see that 3 does not divide 49 completely which means that it is not a factor of 49.
Check-Out:
Comments