Here we are going to discuss, what are the **factors of 62** and how many factors 62 has and what are the **factor pairs of 62**. Here are some methods, showing how to find the factors of 62.

*Actually, Factor is a number which divides any number completely without leaving remainder.*

*Or simply we can say that if we multiply two whole numbers (positive & negative) and it gives a product. Then **the numbers that we multiply, are the factors of the product.*

For example, if we multiply 2 to 31, it gives 62. Here 2 and 31 are positive factors of 62 or we multiply -1 to -62, it gives 62. So -1 and -62 are negative factors of 62.

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## What are the the Factors of 62 ?

Since factors of 62 are the numbers, which divides 62 completely without leaving remainder. So here we are

going to divide 62 by all numbers up to 62. Let’s see the process –

We have to stop the process, if any number of column ‘B’ appears in column ‘A’.

Here we stop the division when 31 appears in column ‘A’, which has already been came in column ‘B’.

Take another example, Factors of 25

In above example, no element of Column ‘B’ appears in Column ‘A’, but we stopped the process

when 5 comes, because on dividing by 5, it produces the same number (5 = 5) .

So we have to stop the process when any element comes in both columns at same level.

And this element will consider as a factor.

*Note :- This situation occurs with a perfect square number, such as 9, 25, 36 etc.*

Hence, all the factors of 62 in above table 1 are : 1, 2, 31, 62

Similarly, negative factors of 62 are : -1, -2, -31, -62

## Factor pairs of 62

As we saw in above table, 1 multiply by 62 gives 62. So (1, 62) or (62, 1) is a factor pair of 62.

Similarly, (2, 31) or (31, 2) is a factor pair of 62.

In example of 25 ; (1, 25) or (25, 1) and (5, 5) are factor pairs.

## Methods of Prime Factors of 62

Here we will discuss, mainly two methods of factorization to find Prime Factors of any number.

### Method #1 (Division Method)

**Step 1 :** Divide the number by the smallest prime number, which divides the number exactly.

**Step 2 :** Divide the quotient again by the smallest prime number. If quotient is not exactly divisible by the

smallest prime number, choose next smallest prime number.

**Step 3 :** Repeat Step 2 again and again till the quotient becomes 1.

**Step 4 :** All the prime numbers used in above process are the prime factors.

Check : Multiply all the prime factors, the multiplication should be the number itself.

Caution : In this method, only prime numbers will be use to divide.

Take example of 62 and 180

In above example of 62,

Step 1 : First of all, we divide 62 by smallest prime number i.e. 2, it gives 31 as quotient and remainder is zero.

(Note – if remainder will not zero, means doesn’t divide exactly, try next prime number to divide)

Step 2: Again we have to divide the quotient 31 by a prime number. Since 31 is also a prime number, so it will divide only itself.

Step 3: We got 1 as a quotient.

Hence, 62 = 2 x 31 = 62. So **62 has only two prime factor i.e. 2 and 31.**

In second example of 180

Step 1 : First of all, we divide 180 by smallest prime number i.e. 2 and we got 90 as quotient and remainder is zero. (Note – if remainder will not zero, means doesn’t divide exactly, try next prime number to divide)

Step 2: Again we divide the quotient 90 by smallest prime number i.e. 2 and we got 45 as quotient.

Again we divide the quotient 45 by smallest prime number i.e. 2, but 2 doesn’t divide 45 exactly. So we try to divide next prime number i.e. 3

Step 3: Repeat step 2 until we got 1 as a quotient.

Hence, 180 = 2 x 2 x 3 x 3 x 5 = 2^{2} x 3^{2}^{ }x 5

So 180 has three prime factor i.e. 2, 3 & 5

### Method #2 (Factor Tree Method)

**Step 1 :** Write a number as root of the tree

**Step 2 :** Find the factors of the number, each factor will be considered as root again (now, we got 2 new root)

**Step 3 :** Repeat step 2 until we can’t factor any more (or until we got prime factor)

**Step 4 :** The end nodes are the prime factors.

We can initiate the tree by choosing any two factors. Here we choose 2 and 31 as factors of 62, and we got the

unique nodes.

Since, 2 and 31 are prime numbers and no more factors can be made. So 62 has two prime factors i.e. 2 and 31.

*Note:- The Factor Tree may be made so many types depends upon choosing the initial and middle factors.*

## Number of factors of 62

To find the number of factors, we use **Method #1 (Division Method).**

In our example, as we saw above 62 = 2 x 31 means 2 to the power 1 multiply 31 to the power 1

** Number of factors is = (power + 1)(power + 1)(power + 1)……….** = (1 + 1)(1 + 1) = 2 x 2 = 4

and if we consider both positive and negative factors, then

total no. of factors = 4 (positive) + 4 (negative) = 8

Take another example, 180 = 2^{2} x 3^{2}^{ }x 5

Number of factors of 60 is = (2 + 1)(2 + 1)(1 + 1) = 3 x 3 x 2 =18

and if we consider both positive and negative factors, then

total no. of factors = 18 (positive) + 18 (negative) = 36

I hope, this step-by-step tutorial will be helpful to understand factorization method of 62.

Try another number 60 for factors.

Take a new look of factorization on Quora.

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