Factors Of 210

We can tell if a number has more than 2 factors just by seeing if a number is a prime number or not. As none of the even numbers except 2 are prime numbers, we can tell that 210 has more than 2 factors. Let us find what the factors are.

Negative factors of 210:  -1, -2, -3, -5, -6, -7, -10, -14, -15, -21, -30, -35, -42, -70, -105 and -210.

Prime factors of 210: The prime factors of 210 are 2,3,5 and 7.

Prime factorization of 210: 2×3×5×7

The sum of factors of 210: 1+2+3+5+6+7+10+14+15+21+30+35+42+70+105+210= 576
 

Children use multiple ways to find factors of a number. Let us look at some ways we can use to find the factors of 210.

• Multiplication Method

• Division Method

• Prime Factor and Prime Factorization
   

In the multiplication method, we find pairs of numbers where the product will be 210. In this process, possible steps will be - 

Step 1: Find all those numbers whose product will be 210.

Step 2: These numbers will be called the factors of 210.

Step 3: Students have to write these pairs of numbers for this method.

List of numbers whose product is 210

210×1= 210

105×2= 210

3×70= 210

42×5= 210

35×6= 210

30×7= 210

21×10= 210

15×14= 210

So the pair of numbers whose product is 210 are (1,210), (2,105), (3,70), (5,42), (6,35), (7,30), (10,21) and (14,15).
 

For the division method, the process of division will go on until the remainder becomes zero.

Step 1: For the division method, always try the smallest number to start with. It is advisable to start dividing the number by 1, then both the number and 1 will be its factors. Example: 210÷1 = 210.

Step 2: Then check with the next number to see whether the number is divided completely without any remainder. Both divisor and quotient are the factors. Example: 210÷5= 42 and so on.

Prime factorization is the process where the number will be a product of prime factors or prime numbers.

Prime Factors Of 210:

The prime factors of 210 are 2,3,5 and 7. We find the prime factors of 210 by two ways.

• Prime Factorization

• Factor Tree

By Prime Factorization: Here we will divide the numbers by the smallest prime number. Till we completely divide the given number. For 210, the steps are like this:

210/5= 42

42/2= 21

21/7= 3

3/3= 1

As 3 is a prime number, it is only divisible by 3. Hence, The prime factorization of the number 210 is 2×3×5×7.
 

This is a very easy method because in many ways it’s almost the same as a prime factorization. We will break down huge numbers in this case to get what we call a factor tree.

Step 1: 210 divided by 5 gives us the answer being 42.

Step 2: 42 divided by 2 gives us 21.

Step 3: 21 divided by 3 gives us 7.

Step 4: 7 divided by 7 gives us 1.

Step 5: This can’t be divided any further.

There are positive and negative factor pairs for a given number. Let us look at these factor pairs.

Positive Factor Pairs: (1,210), (2,105), (3,70), (5,42), (6,35), (7,30), (10,21) and (14,15).

Negative Factor Pairs: (-1,-210), (-2,-105), (-3,-70), (-5,-42), (-6,-35), (-7,-30), (-10,-21) and (-14,-15).
 

• Factor: A factor is a number that divides another number exactly, leaving no remainder. For example, 2 is a factor of 210 because 210 ÷ 2 = 105 with no remainder.

• Prime Factorization: Prime factorization is breaking down a number into its smallest prime factors. For example, the prime factorization of 210 is 2 × 3 × 5 × 7.

• Division Method: This is a method to find factors by dividing the number by smaller numbers in sequence, checking which ones divide evenly.