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Factors

Factors of 70 | How to Find Prime Factors of 70 | Prime Factorization of 70

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

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Factors of 70 | How to Find Prime Factors of 70 | Prime Factorization of 70

Factors of 70 | How to Find Prime Factors of 70 | Prime Factorization of 70

The 70 factors are the digits that can be divided by 70 without having a remainder left. These pair of factors can either be positive or negative. There are a total of eight factors for 70. They are 1, 2, 5, 7, 10, 14, 35, and 70. In this blog, we will explain everything about 70 factors and many more concepts. Scroll down to find out more.

What Are the Factors of 70?

70 is a composite number, which means it has multiple factors. As discussed above, there are 8 factors for the number 6, and they are 1, 2, 5, 7, 10, 14, 35, and 70. The 70 factor has both positive and negative numbers.

Positive FactorsNegative Factors
1-1
2-2
5-5
7-7
10-10
14-14
35-35
70-70

What Are the Factors of 70 in Pairs?

The 70 factors have both positive and negative pairs. Let us see the positive pair and the negative pair of 70 factors:

Positive Pair Factors of 70

The positive 70 pair factors are (1, 70), (2, 35), (5, 14), and (7, 10).

Positive Pair Factors of 70

Negative Pair Factors of 70

The negative 70 pair factors are (-1, -70), (-2, -35), (-5, -14), and (-7, -10).

Negative Pair Factors of 70

How to Find Factors of 70 by Division Method?

We can also use the division method to find out the 70 factors. To find factors of 70, using the division method, we need to divide the number 70 with a sequence of natural numbers from 1 to 70. The numbers which don’t leave any remainder are the numbers known as factors of 70. Those numbers which leave a remainder are the numbers that are not factors of 70.

  • 70 ÷ 1 = 70 (Remainder = 0)
  • 70 ÷ 2 = 35 (Remainder = 0)
  • 70 ÷ 5 = 14 (Remainder = 0)
  • 70 ÷ 7 = 10 (Remainder = 0)
  • 70 ÷ 10 = 7 (Remainder = 0)
  • 70 ÷ 14 = 5 (Remainder = 0)
  • 70 ÷ 35 = 2 (Remainder = 0)

Therefore, we can conclude that 1, 2, 5, 7, 10, 14, 35, and 70 are 70 factors.

Prime Factorization of 70

The composite numbers will always have prime numbers as their prime factors. The steps to find the 70 prime factors using the prime factorization method have been provided below:

  • Step 1: Firstly, we will divide 70 with 2 as it’s the smallest prime number.
    70 ÷ 2 = 35
  • Step 2: Now, since we cannot divide 35 by 2, we will divide with the next smallest prime number which 35 can be divided by i,,e 5.
    35 ÷ 5 = 7
  • Step 3: Now, since we cannot divide 7 by 5, we will divide with the next smallest prime number which 7 can be divided by i.,e 7.
    7 ÷ 7 = 1

Therefore, we obtained 1 at the end. This says that the 70 prime factors are 2 x 5 x 7.

2, 5, and 7 prime factors of 70.

Here is an image for you so you can understand the concept easily.

Prime Factorization of 70

Write the Factor Tree of 70

The steps to find a factor tree of 70 are given below:

  • Step 1: Firstly, write the number 70 at the top of the factor tree.
  • Step 2: Now, as a part of the tree’s branches, write down the pair factor of 70. The pair factor we have used here is 7 and 10.
  • Step 3: Since seven is a prime number, we can no longer separate it.
  • Step 4: But as 10 is a composite number, we can split it into 2 and 5.
  • Step 5: As both 2 and 5 are prime numbers, we cannot separate them. That’s it!

Hence, the factors of all the numbers are prime numbers. Circling all the branches gives us factors 2, 5, and 7, Therefore, the prime factors of 70 using a factor tree are 2 X 5 X 7 = 70.

The factor tree of 70 is given below:

Factor tree of 70

Solved Examples on Factors of 70

The solved examples on factors of 70 are given below:

What is the sum of all the factors of 70? 
To find the sum of all the factors, we need to add all 70 factors. 
Adding 1 + 2 + 5 + 7 + 10 + 14 + 35 + 70 equals 144. 
Hence, the sum of all 70 factors is 144.

What are the factors and prime factors of 70? 
Factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70. 
The prime factors of 70 are 2, 5, and 7.

What’s the highest common factor between 70 and 90? 
The 70 factors are 1, 2, 5, 7, 10, 14, 35, and 70. 
And the 90 factors are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. 
If we see the GFC of 10 is the most common factor.

What’s the highest common factor between70 and 25? 
Factors of 70 are 1, 2, 5, 7, 10, 14, 35, and 70 
And the 25 factors are 1, 5, and 25. 
If we see the GFC of 5 is the most common factor.

FAQs on Factors of 70

List all the factors of 70
1. 2, 5, 7, 10, 14, 35, and 70 are the 70 factors.

What are the composite factors of 70? 
Composite numbers are those that are described as whole digits and have three or more whole number factors. Hence 70 has 10, 14, 35, and 70 as composite factors.

What are the factors of 70 in pairs? 
(1, 70), (2, 35), (5, 14), and (7, 10) are the 70 factors in pairs.

What are the positive factors for 70? 
1, 2, 5, 7, 10, 14, 35, and 70 are positive seventy factors.

What are the factors of 70 that are not prime numbers?
The factors of 70 that are not prime numbers are 1, 14, 35, 10 and 70.

Now that you have all the necessary information about factors of 70 and we hope this detailed article is helpful to you. If you have any questions related to this page or in general about 70 factors, ping us through the comment box below and we will get back to you as soon as possible.

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Prerit Jain

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