Here we are going to discuss, what are the **factors of 70** and how many factors 70 has and what are the **factor pairs of 70**. Here are some methods, showing how to find the factors of 70.

*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 5 to 14, it gives 70. Here 5 and 14 are positive factors of 70 or we multiply -2 to -35, it gives 70. So -2 and -35 are negative factors of 70.

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## What are the Factors of 70 ?

Since factors of 70 are the numbers, which divides 70 completely without leaving remainder. So here we are

going to divide 70 by all numbers up to 70. 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 10 appears in column ‘A’, which has already been came in column ‘B’.

Hence, all the factors of 70 in above table are : 1, 2, 5, 7, 10, 14, 35, 70

Similarly, negative factors of 55 are : -1, -2, -5, -7, -10, -14, -35, -70

Take another example, **Factors of 49**

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

when 7 comes, because on dividing by 7, it produces the same number (7 = 7) .

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, 16, 25, 36, 49 etc.*

## Factor pairs of 70

As we saw in above table, 1 multiply by 70 gives 70. So (1, 70) or (70, 1) is a factor pair of 70.

Similarly, (2, 35), (5, 14) and (7, 10) are another factor pairs of 70.

In example of 49 ; (1, 49) or (49, 1) and (7, 7) are factor pairs.

## Methods of Prime Factors of 70

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 70 and 90

In above example of 70,

Step 1 : First of all, we divide 70 by smallest prime number i.e. 2, it gives 35 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 35 by a prime number i.e. 2. But 2 doesn’t divide 35 completely. So we have try to divide by next prime number i.e. 3. This time also 35 doesn’t divide completely. Try next prime number i.e. 5.

Step 3: On divided by 5, it gives 7 as quotient and remainder is zero.

Step 4: Since 7 is a prime number, hence 7 will divide by itself only. So we divide 7 by 7. We got 1 as a quotient.

Hence, 70 = 2 x 5 x 7. So 70** has three prime factor i.e. 2 , 5 and 7.**

In second example of 90

Step 1 : First of all, we divide 90 by smallest prime number i.e. 2 and we got 45 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 45 by smallest prime number i.e. 2. But 2 doesn’t divide 45 completely. So we have try to divide by next prime number i.e. 3 and we got 15 as quotient. (Repeat step 2 until we got 1 as a quotient.)

Hence, 90 = 2 x 3 x 3 x 5 = 2 x 3^{2} x 5

So 90 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.

**Factor Tree of 70**

In First Tree ( see above figure), We can initiate the tree by choosing any two factors. Here we choose 5 and 14 as factors of 70.

Further, we have to divide these nodes. Since 5 is a prime number, so it can’t be split further.

and 14 can be split into two factors 2 and 7.

Here we got, 2, 5 and 7 as unique nodes. So 70 has three prime factors i.e. 2, 5 and 7.

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

## Number of factors of 70

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

In our example, as we saw above 70 = 2 x 5 x 7 means 2 to the power 1 multiply 5 to the power 1 multiply 7 to the power 1

** Number of factors is = (power + 1)(power + 1)(power + 1)……….** = (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2= 8

if we consider both positive and negative factors, then

total no. of factors = 8 (positive) + 8 (negative) = 16

Take another example, 90 = 2 x 3 x 3 x 5 = 2 x 3^{2} x 5

Number of factors of 90 is = (1 + 1)(2 + 1)(1 + 1) = 2 x 3 x 2 =12

and if we consider both positive and negative factors, then

total no. of factors = 12 (positive) + 12 (negative) = 24

I hope, this step-by-step tutorial will be helpful to understand factorization method of 75.

Try another number 75 for factors.

Take a another look of factorization on Quora.

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