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Factors of 70

Factors of 70 are the list of integers that we can split evenly into 70. There are 8 factors of 70, which are 1, 2, 5, 7, 10, 14, 35, and 70. Here, 70 is the biggest factor. The sum of all factors of 70 is 144. Its Prime Factors are 1, 2, 5, 7, 10, 14, 35, 70 and (1, 70), (2, 35), (5, 14) and (7, 10) are Pair Factors.

Factors of 70: 1, 2, 5, 7, 10, 14, 35 and 70
Negative Factors of 70: -1, -2, -5, -7, -10, -14, -35 and -70
Prime Factors of 70: 2, 5, 7
Prime Factorization of 70: 2 × 5 × 7 = 2 × 5 × 7
Sum of Factors of 70: 144

1.	What Are the Factors of 70?
2.	How to Calculate the Factors of 70?
3.	Factors of 70 by Prime Factorization
4.	Factors of 70 in Pairs
5.	Important Notes
6.	FAQs on Factors of 70

What Are the Factors of 70?

Factors of a number n are the numbers that completely divide the number n. It implies that if the remainder is 0 when n is divided by a, then a is a factor of n.

Factors of a number

We are talking about factors of the number 70. Let's first see the numbers that completely divide 70.
The numbers that divide 70 completely are 1, 2, 5, 7, 10, 14, 35, and 70.

How to Calculate the Factors of 70?

Factors of any number n can be calculated by many methods; one of the methods is dividing the number by the smallest of the factors.
Factors of number 70 can be calculated as follows:

Step 1: Write the smallest two factors of 70 (except for 1). The smallest two factors of 70 are 2 and 5.
Step 2: Divide 70 by 2 and 5.
70/2 = 35 and 70/5 = 14
So, 2, 5, 14, and 35 are the factors of 70.
Step 3: Now take the next factor of 70.
The next factor of 70 is 7.
Divide 70 by 7.
70/7 = 10
So, 2, 5, 7, 10, 14, and 35 are the factors of 70.
Step 4: Include 1 and the number itself to the factors.

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

To understand the concept of finding factors by prime factorization better, let us take a few more examples.

Factors of 36 - The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 35 - The factors of 35 are 1, 5, 7, 35
Factors of 270 - The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
Factors of 150 - The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Factors of 90 - The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 24 - The factors of 1, 2, 3, 4, 6, 8, 12, 24

Factors of 70 by Prime Factorization

The prime factorization method to calculate factors of any number is one of the most important methods. Many students prefer using prime factorization while performing calculations. In the prime factorization method, we can only factorize a number into its prime factors. Prime numbers are the numbers that have only two factors, 1 and the number itself.

For example, 2, 3, 5, 7, 11, 13, and so on.

Factor tree of 70

Prime factors of 70 are 2, 5, and 7.

70 = 2 × 5 × 7

Let's write all the factors of 70 using prime factors

Step 1: Take the prime factors of 70: 2, 5, and 7.
Step 2: Multiply the prime factors of 70, taking two at a time.
2 × 5 = 10
2 × 7 = 14
5 × 7 = 35
Factors obtained are 10, 14, and 35.
Step 3: Write all the factors of the number 70.
1, 2, 5, 7, 10, 14, 35, 70
Now that we have done the prime factorization of our number, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not?
And as you might have already guessed, for prime numbers, there are no other factors.

Factors of 70 in Pairs

Pair factors of number n are the set of two numbers which when multiplied together give the number n.

Factors of 70 are: 1, 2, 5, 7, 10, 14, 35, 70
Factors of 70 in pairs are: (1, 70), (2, 35), (5, 14), (7, 10)

1 × 70 = 70
2 × 35 = 70
5 × 14 = 70
7 × 10 = 70

Factors of 70 in pairs

Pairs of negative factors of 70 are: (-1, -70), (-2, -35), (-5, -14), (-7, -10)

-1 × -70 = 70
-2 × -35 = 70
-5 × -14 = 70
-7 × -10 = 70

Important Notes:

Every number has at least two factors, i.e., 1 and the number itself.
There are no factors of a number n between (n, n/2).
Numbers that have more than 2 factors are called composite numbers.

Challenging Questions:

Find the greatest number of 4 digits and the least number of 5 digits that have as their G.C.F. as 70.
A function f(x) = x² +bx + 5 has a factor (x -1). Find the value of b.

Solved Examples

Example 1: Sam wants to empty two buckets full of water with capacities of 140 liters and 70 liters. He needs to empty the buckets with the help of a glass. What capacity of glass should he choose so that no water remains in any of the buckets.

Solution:

Given:

The capacity of one bucket = 140 liters
The capacity of the other bucket = 70 liters

To find the capacity of glass we need to calculate the HCF (Highest Common Factor) of 70 and 140.

70 = 1 × 2 × 5 × 7
140 = 1 × 2 × 2 × 5 × 7

HCF of 70 and 140 = 2 × 5 × 7 = 70
Hence, Sam will use a glass of capacity 70 liters.
Example 2: John wants to find the common factors of 70, 420, and 560.

Solution:

Factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70
Factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
Factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560

Hence, the common factors of 70, 420, and 560 are 1, 2, 5, 7, 10, 35, and 70.
Example 3: Julia wants to add a number to 6 so that it becomes a factor of 70. What numbers can she add?

Solution:

Let's suppose she adds x to 6

So (x + 6) is a factor of 70.
Let's write down all the factors of 70 greater than 6:

7, 10, 14, 35, 70

x + 6 = 7
x + 6 = 10
x + 6 = 14
x + 6 = 35
x + 6 = 70

Hence, Julia can add 1, 4, 8, 29, or 64 to 6 to get a factor of 70.

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FAQs on Factors of 70

What are the Factors of 70?

The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70 and its negative factors are -1, -2, -5, -7, -10, -14, -35, -70.

What are the Prime Factors of 70?

The prime factors of 70 are 2, 5, 7.

What is the Greatest Common Factor of 70 and 47?

The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70 and the factors of 47 are 1, 47. 70 and 47 have only one common factor which is 1. This implies that 70 and 47 are co-prime.

Hence, the Greatest Common Factor (GCF) of 70 and 47 is 1.

What is the Sum of the Factors of 70?

Sum of all factors of 70 = (2^{1 + 1} - 1)/(2 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (7^{1 + 1} - 1)/(7 - 1) = 144

What are the Common Factors of 70 and 15?

Since, the factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70 and the factors of 15 are 1, 3, 5, 15.
Hence, [1, 5] are the common factors of 70 and 15.

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