Factors Of 49 – With Division and Prime Factorization

Factors of 49

Factors Of 49

Mathematically, factors of 49 are real numbers that can divide an original number equally or evenly. In another way, if two numbers result in the same number, then they become factors. 

It has more than two factors since 49 is a composite number. By using the division method, we can find these factors. Similarly, we can also determine the prime factors by using the prime factorization method. 

Next, we will find 49’s prime factors and pair factors.

How to Find Factors of 49?

The factor is the number that divides the original number (here, 49), completely.

49 ÷ 1 = 49     

49 ÷ 7 = 7  

49 ÷ 49 = 1

Consequently, 1, 7, and 49 are the factors of 49.

factors of 49

What are the Factors of -49?

Similarly, factors of -49: -1, -7, and -49.

To get the product -49, multiply two numbers as follows:

-1 x  49 =  -49    &   1 x -49 =  -49

-7 x  7 = -49     &  7 x  -7 = -49

Pair Factors of 49

Factors in pairs are those numbers that, when multiplied together, return the original number (in this case 49). 

  • 1 × 49 = 49
  • 7 × 7 = 49

Thus, (1, 49) and (11, 13) are the positive pair factors.

In the case of the negative pair factors;

  • -1 × -49 = 49
  • -7 × -7 = 49

Accordingly, the negative pair factors are (-1, -49) and (-7, -7).

factors of 49 in pairs

Prime Factorization of 49

Numbers that divide 49 completely are its prime factors. For the prime factors, below are the prime numbers between 1 and 50.

List of prime numbers (1 to 50) :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

According to the above, 49 is completely divisible by 7. Therefore, 7 is its smallest prime factor.

49/7 = 7

Since 7 is a prime number, it can be divided by either 1 or itself. 

7/7 = 1

There can be no further division since we already have a dividend of 1.

Accordingly,

Prime factorization of 49 = 7 x 7

Factors of 49 by prime factorization

Solved Examples

Q.1: If 7 flowers are bought for Rs.49. Then what is the cost of each flower?

Number of flowers bought = 7

The cost of seven flowers is = Rs. 49

Each flower costs = 49/7 = 7

As a result, each flower cost Rs. 7.

Q.2: Find the sum of all the factors of 49. Also, find the average.

49 has the factors 1, 7, and 49.

The sum is 1 + 7 + 49 = 57

As a result, 157 is the required sum.

Using the sum of the factors, divide the total number of factors by the average of the factors.

Thus, 

Average = 157/3 = 52.33

Q.3: What is the greatest common factor of 45 and 49?

Here are the factors of both numbers.

49 → 1, 7, 49

45 → 1, 3, 5, 9, 15, 45

Therefore, there is only 1 common factor.

Q.4: What is the GCF of 49 and 84?

There are three factors in 49: 1, 7, and 49.

The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Comparing 49 and 84, 7 is the greatest common factor.

GCF (49, 84) = 7

More Factors:

Factors of 100=1, 2, 4, 5, 10, 20, 25, 50 and 100.Factors Of 120= 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.
Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144.Factors Of 72= 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Factors of 49=  1, 7, 49 

FAQs

What are the factors of 49?

There are three factors of 49 in total. They are 1, 7, and 49.

As a product of prime factors, how is 49 represented?

49 has the following prime factorization:

49 = 7 x 7 = 72

How many multiples of 49 are there?

49, 98, 147, 196, 245, 294, 343, 392, 441 and 490 are the first 10 multiples of 49.

Does 3 have a factor of 49?

No, 3 isn’t a factor, 49. 3 cannot divide 49.

49 is a prime number, or not?

No, 49 has more than two factors, so it is a composite number.

Does 49 make a perfect square?

Yes, 49 is a perfect square since its root is a whole number.

√49 = 7

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