[Maths Class Notes] on Factors Of 49 Pdf for Exam

49 is a composite number and all its factors are integers that can be divided evenly into 49. 

But tell me “What is a factor?” A factor is a number that divides another number without leaving a remainder. For example, 5 is a factor of 30 as it divides 30 exactly at 6 with no remainder. Now, the most important is “ What are the factors of 49?” so, we will answer this question straightforwardly and simply. The factors of 49 are 1, 7, and 49. 

 

Now, another important question that arises is “How do we know that these are the correct factors of 49?” the answer to this question is given under the next heading.

 

How Can We Find The Factors Of 49?

There are two basic methods to know which number can be the correct factor. These two methods to recognize a factor are:

1. We can use the test of divisibility to find a factor of a number.

2. Simply divide and see if the factor divides the number without leaving any remainder. We know the factors of 49 are 1, 7, and 49. Let us check if we are correct. 

49 ÷ 1 = 49 (no remainder)

49 ÷ 7 = 7 (no remainder)

49 ÷ 49 = 1 (no remainder)

Therefore, 1, 7, and 49 are all factors of 49. 

 

How Many Factors Of 49 Are There?

If we see the performed divisions above, then we can conclude that there are only 3 factors of 49. 1, 7 and 49 are the common factors of 49. These factors divide 49 evenly and without leaving any remainders. 

 

Pair Factors Of 49

Pair factors are combinations of any two factors which when multiplied together gives 49 as the product. Here we can see all the Positive pair factors of 49. 

1 x 49 = 49     therefore, we can say 1 and 49 are pair factors.

7 x 7 = 49       therefore, we can say 7 and 7 are pair factors.

49 x 1 = 49     therefore, we can say 49 and 1 are pair factors.

 

Prime Factorization

We already know what a prime factorization is but let us refresh it. A prime factorization is a method where a set of prime numbers are multiplied together to produce the original number. Now,  let us directly jump into the prime factorization of 49. 7 x 7 = 49 is the prime factorization of 49. We can also write it as 72 72and thus it is also a square number. 

 

Factor Tree of 49

A factor tree is a graphical representation of a tree with numbers. It represents the factors of a number as well as the sub-factors of the factors of the number. Here is an example of a factor tree of 49 for you. 

 

(Image to be added soon)

 

Solved Examples

Example 1. find the factors of the following number: 

1. 40

2. 36

3. 72

4. 98

5. 25

6. 104

7. 352

8. 728

9. 612

10. 414

 

Solution Finding The Factors Of The Following Numbers:

1. Factors of 40

Factors of 40 are 1,2,4,5,8,10,20,40

2. Factors of 36

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

3. Factors of 72 

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

4. Factors of 98 

Factors of 98 are 1, 2, 7, 14, 49 and 98.

5. Factors of 25 

 Factors of 25 1, 5, and 25.

6. Factors of 104

Fators of 104 are 1, 2, 4, 8, 13, 26, 52 and 104.

7. Factors of 352

 Factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176 and 352.

8. Factors of 728 

Factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364 and 728.

9. Factors of 612 

Factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306 and 612.

10. Factors of 414 are

Factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207 and 414.

Example 2. Find the Prime Factorization of 32.

Solution Prime factorization is a set of prime numbers that can divide a number without any remainder. Thus, the prime factorization of 32 is:

32 = 2 x 2 x 2 x 2 x 2 = 32.

 

Prime Factors of 49

7 x 7 are the prime factors of 49.

The prime factors of a positive integer are the prime numbers that divide that integer perfectly in number theory. The prime factorization of any positive integer is the list of the integer’s prime factors, together with their multiplicities; integer factorization is the method of determining these factors. To get the prime factors of a number, type it into the input box below.