Factors Of 136

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

Negative factors of 136: -1, -2, -4, -8, -17, -34, -68 and -136.

Prime factors of 136: The prime factors of 136 are 2 and 17.

Prime factorization of 136: 2×2×2×17

The sum of factors of 136: 1+2+4+8+17+34+68+136= 270
 

Children use multiple ways to find factors of a number. Let us look at some ways we can use to find the factors of 136

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• Multiplication Method

• Division Method

• Prime Factor and Prime Factorization
   

In the multiplication method, we find pairs of numbers where the product will be 136. In this process, possible steps will be - 

Step 1: Find all those numbers whose product will be 136.

Step 2: These numbers will be called the factors of 136.

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

List of numbers whose product is 136

136 × 1= 136

68 × 2= 136

34×4= 136

17×8= 136

So the pair of numbers whose product is 136 are (1,136), (2,68), (4,34) and (8,17).
 

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: 136÷1 = 136

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: 136÷2 = 68 and so on.
 

Prime factorization is the process where the number will be a product of prime factors or prime numbers.
Prime Factors Of 136

The prime factors of 136 are 2 and 17. We find the prime factors of 136 by two ways.

By Prime Factorization: Here we will divide the numbers by the smallest prime number. Till we completely divide the given number. For 136, the steps are like this:

136/2= 68

68/2= 34

34/2= 17

17/17= 17

As 17 is a prime number, it is only divisible by 17. Hence, The prime factorization of the number 136 is 2×2×2×17.
 

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: 136 divided by 2 gives us the answer being 68.

• Step 2: 68 divided by 2 gives us 34.

• Step 3: Again, we break 34 into 2s, and we get 17 as our answer for 34. 

• Step 4: This we can’t divide further into, since 17 is a prime number. 

Factor Pairs For 136 :There are positive and negative factor pairs for a given number. Let us look at these factor pairs.

Positive Factor Pairs: (1,136), (2,68), (4,34) and (8,17).

Negative Factor Pairs: (-1,-136), (-2,-68), (-4,-34) and (-8,-17).
 

• Factors: Divisible of a given number, without remainder. The factors of 136 would be 1,2, 4, 8, 17, 34, 68 and 136.

• Prime Factorization: A product of prime numbers written as a number — 136 is a prime factorization of 2×2×2×17.

• Square Root: It is an integer or a decimal, something which, multiplied by itself, gives you the original number. In this case, we can write that the square root of 136 is around 11.66.

• Prime Factors: Numbers which divide a given number exactly. Factors prime of 136 are: 2, 17.