Factors of 49: Method, Total Number of Factors – Mindspark.

What do we mean by Factors of 49?

The factors of a number x  are the numbers that completely divide x with zero as a remainder. It means that if y divides x and the remainder is 0 then we say that y is a factor of x.

Factors of 49 i.e, the numbers which completely divide 49 are 1, 7, 49. Therefore 49 has a total of 3 factors.

Factors of 49

The easiest way to calculate the factors of any number is by first dividing the number by its smallest factor. So the number which will divide the number completely and the quotient will be the factor( This is also known as Pair of the factors). We will repeat this process till we find all the factors.

We know that 1 will be the factor of every number, so 

\frac{49}{1}=49. Therefore 1 and 49 are the factors of 49. Now we’ll do it with numbers greater than one.

\frac{49}{7}=7

Therefore the factors of 49 are 1, 7, 49.

Factors of 49 by Tree Method

The tree method is also known as Prime Factorisation. Prime Factorisation of a number means the way of writing the numbers by using its prime factors. For example, we can write 49 as 7 × 7. 

We call it a tree method because the number of which we have to find the factors is the highest factor of itself (highest branch) and the rest of the factors are lower than the number itself and when we simplify it we get the prime numbers (which are one of the smallest factors of the number) and this forms a shape like a tree as we are branching out 49 into its prime factors.

49  can be written with prime factorisation as-

     49=7^{2}
\Rightarrow 49=7 \times 7

Factors of 49 in the form of Pairs

We can write the factors in the form of pairs. The pair means that when we will multiply the two numbers well get the result as 49 –

1 × 49 = 49

7 × 7 = 49

Therefore the Pair Factors of 49  are (1, 49) and (7, 7).

Factors of a number can be negative too but only when they are in pairs and negative as when we multiply the two numbers we get the result as 49.

−1 × −49 = 49

−7 × −7 = 49

Therefore the negative Pair factors of 49 are (−1,−49) and (−7,−7).

Examples 

1. Which of the following are factors of 49?

    5,6,7,14 

Solution: Only 7 is a factor of 49 as it completely divides 49. 

5, 6 and 14 are not factors of 49 as when we divide 49 from 5, 6 and 14 we do not get natural numbers.

49/5 = 9.8 

49/6 = 8.167

49/14 = 3.5

2. Is 196 a factor of 49? 

Solution: No, 196 is not a factor of 49. The highest factor of a number will be the number itself. 196 is a multiple of 49 as 49 x 4= 196.

POINTS TO REMEMBER

• 1 is a factor of every number therefore it is known as a universal factor and the smallest factor of a number. 
• The highest factor of a number will be the number itself.
• If a number has more than two factors then it is called a non-prime (composite) number. Therefore 49 is a composite number.