Factors Of 49 | With Easy Division and Prime Factorization

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.

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).

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

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 and 3. 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

Prime Factors of 3 = 1 and 3.

The sum is= 4

Average= 2

Q.3: What is the common factor of 24 and 56?

Here are the factors of both numbers.

Prime Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24.

Prime Factors Of 56= 1, 2, 4, 7, 8, 14, 28, and 56

Therefore, there are only 1, 2, 4, and 8 common factors.

Q.4: What is the GCF of 49 and 72?

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

The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

Comparing 49 and 82, 1 is common.

GCF (49, 72) = 1

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