Factors Of 240

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 240 has more than 2 factors. Let us find what the factors are.

Negative factors of 240: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -30, -40, -48, -60, -80, -120 and -240.

Prime factors of 240: The prime factors of 240 are 2,3 and 5.

Prime factorization of 240: 2×2×2×2×3×5.

The sum of factors of 240: 1+2+3+4+5+6+8+10+12+15+16+20+24+30+40+48+60+80+120+240= 744
 

Children use multiple ways to find factors of a number. Let us look at some ways we can use to find the factors of 240.

• Multiplication Method

• Division Method

• Prime Factor and Prime Factorization

In the multiplication method, we find pairs of numbers where the product will be 240. In this process, possible steps will be - 

Step 1: Find all those numbers whose product will be 240.

Step 2: These numbers will be called the factors of 240.

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

List of numbers whose product is 240

240×1= 240

120×2= 240

80×3= 240

60×4= 240

48×5= 240

40×6= 240

30×8= 240

24×10= 240

20×12= 240

16×15= 240

So the pair of numbers whose product is 240 are (1,240), (2,120), (3,80), (4,60), (5,48), (6,40), (8,30), (10,24), (12,20) and (15,16).
 

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: 240÷1 = 240.

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: 240÷5= 48 and so on.

Prime Factors Of 240: The prime factors of 240 are 2,3 and 7. We find the prime factors of 240 by two ways.

Prime Factorization:  Here we will divide the numbers by the smallest prime number. Till we completely divide the given number. For 240, the steps are like this:

240/5= 48

48/2= 24

24/2= 12

12/2= 6

6/2= 3

3/3= 1

As 3 is a prime number, it is only divisible by 3. Hence, The prime factorization of the number 240 is 2×2×2×2×3×5.
 

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: 240 divided by 5 gives us the answer being 48.

Step 2: 48 divided by 2 gives us 24.

Step 3: 24 divided by 2 gives us 12.

Step 4: 12 divided by 2 gives us 6.

Step 5: 6 divided by 2 gives us 3.

Step 6: 3 divided by 3 gives us 1.

Step 7: 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: (1,240), (2,120), (3,80), (4,60), (5,48), (6,40), (8,30), (10,24), (12,20) and (15,16).

Negative Factor Pairs:(-1,-240), (-2,-120), (-3,-80), (-4,-60), (-5,-48), (-6,-40), (-8,-30), (-10,-24), (-12,-20) and (-15,-16).
 

• Prime Factorization: The process of expressing a number as the product of its prime factors. For instance, the prime factorization of 240 is 24×3×5.

• Greatest Common Factor (GCF): The largest factor that two or more numbers share. For 240 and 60, the GCF is 60.

• Whole Numbers: Non-negative numbers without fractions or decimals, including 0. Examples are 0, 1, 2, 3, etc.