Factors of 35: Method, Total Number of Factors – Mindspark.

What do we mean by Factors of 35?

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 35 i.e, the numbers which completely divide 35 are 1, 5, 7, 35. Therefore 35 has a total of 4 factors.

Factors of 35

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 is the factor of every number, so 

\frac{35}{1}=35.

Now we’ll do it with numbers greater than one.

\frac{35}{5}=7

Therefore the factors of 35 are 1, 5, 7, 35.

Factors of 35 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 35 as 5 × 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 35 into its prime factors.

35  can be written with prime factorisation as-

35 =  5 × 7

Factors of 35 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 35 –

1 × 35 = 35

5 × 7 = 35

Therefore the Pair Factors of 35  are (1, 35) and (5, 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 35.

−1 × −35 = 35

−5 × −7 = 35

Therefore the negative Pair factors of 35 are (−1,−35) are (−5,−7).

Examples 

1. Which of the following are factors of 35?

     5,7,10,14 

Solution: 5 and 7 are factors of 35 as they completely divide 35. 

10 and 14 are not factors of 35 as when we divide 35 from 10 and 14 we do not get natural numbers.

35/10 = 3.5

35/14 = 2.5

2. Is 105 a factor of 35? 

Solution: No, 105 is not a factor of 35. The highest factor of a number will be the number itself. 105 is a multiple of 35 as 35 x 3= 105.

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.
• A number having more than two factors then is called a composite number. Therefore 35 is a composite number.