 # Factors Of 49

## What Are The Factors Of 49?

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 Common 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 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.

### Example 1. find the factors of the following number:

i) 40

ii) 36

iii) 72

iv) 98

v) 25

vi) 104

vii) 352

viii) 728

ix) 612

x) 414

Solution Finding the factors of the following numbers:

## i) Factors of 40 are

 2 40 2 20 2 10 5 5 1

## ii) Factors of 36 are

 2 36 2 18 3 9 3 3 1

## iii) Factors of 72 are

 2 72 2 36 2 18 3 9 3 3 1

## iv) Factors of 98 are

 2 98 7 49 7 7 1

## v) Factors of 25 are

 5 25 5 5 1

## vi) Factors of 104 are

 2 104 2 52 2 26 13 13 1

## vii) Factors of 352 are

 2 352 2 176 2 88 2 44 2 22 11 11 1

## viii) Factors of 728 are

 2 728 2 364 2 182 7 91 13 13 1

## ix) Factors of 612 are

 2 612 2 36 2 18 3 9 3 3 1

## x) Factors of 414 are

 2 414 3 27 3 9 3 3 1

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.

1. What are the Multiples of 49?

Let us Find the first 49 multiples of 49.

49 x 1 = 49                    49 x 2 =98                     49 x 3 = 147                    49 x 4 = 196

49 x 5 = 245                  49 x 6 = 294                  49 x 7 = 343                    49 x 8 = 392

49 x 9 = 441                  49 x 10 = 490                49 x 11 = 539                  49 x 12 = 588

49 x 13 = 637                49 x 14 = 686                49 x 15 = 735                  49 x 16 = 784

49 x 17 = 833                49 x 18 = 882                49 x 19 = 931                  49 x 20 = 980

49 x 21 = 1029              49 x 22 = 1078              49 x 23 = 1127                49 x 24 = 1176

49 x 25 = 1225              49 x 26 = 1274              49 x 27 = 1323                49 x 28 = 1372

49 x 29 = 1421              49 x 30 = 1470              49 x 31 = 1519                49 x 32 = 1568

49 x 33 = 1617              49 x 34 = 1666              49 x 35 = 1715                49 x 36 = 1764

49 x 37 = 1813              49 x 38 = 1862              49 x 39 = 1911                49 x 40 = 1960

49 x 41 = 2009              49 x 42 = 2058              49 x 43 = 2107                49 x 44 = 2156

49 x 45 = 2205              49 x 46 = 2254              49 x 47 = 2303                49 x 48 = 2352

49 x 49 = 2401

2. What is the Sum of All the Factors of 49?

The sum of all the factors of 49 can be achieved by adding all the factors of 49.

So let us add all the factors of 49 to get the sum of all the factors of 49.

Factors of 49 = 1, 7, and 49.

Adding them together: 1 + 7 + 49 = 57

Therefore, the sum of all the factors of 49 is 57.

3. Is 49 a Prime Number or a Composite Number? What is the Difference Between a Prime Number and a Composite Number?

It will be better if we first know the answer of the last question then come back to the first question. So the second question is “What is the difference between a prime number and a composite number?”. Well, if a number is divisible by only 1 and the number itself then it is a prime number. For example, 2, 3, 5, 7, 11 and so on. These numbers cannot be divided by any other number except 1 and the number themselves. On the other hand, if a number is divisible by more than two numbers, it will be called a composite number. For example, 4, 6, 8, 10, and so on. 4 can be divided by 1, 2, and 4, therefore it is a composite number. 6 can be divided by 1, 2, 3, and 6, thus therefore it is also a composite number. Now, coming back to the first question, 49 is a composite number as it can be divided by more than two numbers.