GCF of 10 and 70
GCF of 10 and 70 is the largest possible number that divides 10 and 70 exactly without any remainder. The factors of 10 and 70 are 1, 2, 5, 10 and 1, 2, 5, 7, 10, 14, 35, 70 respectively. There are 3 commonly used methods to find the GCF of 10 and 70  prime factorization, long division, and Euclidean algorithm.
1.  GCF of 10 and 70 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is GCF of 10 and 70?
Answer: GCF of 10 and 70 is 10.
Explanation:
The GCF of two nonzero integers, x(10) and y(70), is the greatest positive integer m(10) that divides both x(10) and y(70) without any remainder.
Methods to Find GCF of 10 and 70
The methods to find the GCF of 10 and 70 are explained below.
 Long Division Method
 Using Euclid's Algorithm
 Listing Common Factors
GCF of 10 and 70 by Long Division
GCF of 10 and 70 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
 Step 1: Divide 70 (larger number) by 10 (smaller number).
 Step 2: Since the remainder = 0, the divisor (10) is the GCF of 10 and 70.
The corresponding divisor (10) is the GCF of 10 and 70.
GCF of 10 and 70 by Euclidean Algorithm
As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.
Here X = 70 and Y = 10
 GCF(70, 10) = GCF(10, 70 mod 10) = GCF(10, 0)
 GCF(10, 0) = 10 (∵ GCF(X, 0) = X, where X ≠ 0)
Therefore, the value of GCF of 10 and 70 is 10.
GCF of 10 and 70 by Listing Common Factors
 Factors of 10: 1, 2, 5, 10
 Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
There are 4 common factors of 10 and 70, that are 1, 2, 10, and 5. Therefore, the greatest common factor of 10 and 70 is 10.
☛ Also Check:
 GCF of 48 and 120 = 24
 GCF of 7 and 9 = 1
 GCF of 20 and 40 = 20
 GCF of 16 and 60 = 4
 GCF of 63 and 72 = 9
 GCF of 27 and 72 = 9
 GCF of 48 and 56 = 8
GCF of 10 and 70 Examples

Example 1: Find the GCF of 10 and 70, if their LCM is 70.
Solution:
∵ LCM × GCF = 10 × 70
⇒ GCF(10, 70) = (10 × 70)/70 = 10
Therefore, the greatest common factor of 10 and 70 is 10. 
Example 2: For two numbers, GCF = 10 and LCM = 70. If one number is 70, find the other number.
Solution:
Given: GCF (z, 70) = 10 and LCM (z, 70) = 70
∵ GCF × LCM = 70 × (z)
⇒ z = (GCF × LCM)/70
⇒ z = (10 × 70)/70
⇒ z = 10
Therefore, the other number is 10. 
Example 3: The product of two numbers is 700. If their GCF is 10, what is their LCM?
Solution:
Given: GCF = 10 and product of numbers = 700
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 700/10
Therefore, the LCM is 70.
FAQs on GCF of 10 and 70
What is the GCF of 10 and 70?
The GCF of 10 and 70 is 10. To calculate the greatest common factor (GCF) of 10 and 70, we need to factor each number (factors of 10 = 1, 2, 5, 10; factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70) and choose the greatest factor that exactly divides both 10 and 70, i.e., 10.
How to Find the GCF of 10 and 70 by Prime Factorization?
To find the GCF of 10 and 70, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 70 = 2 × 5 × 7.
⇒ Since 2, 5 are common terms in the prime factorization of 10 and 70. Hence, GCF(10, 70) = 2 × 5 = 10
☛ What is a Prime Number?
How to Find the GCF of 10 and 70 by Long Division Method?
To find the GCF of 10, 70 using long division method, 70 is divided by 10. The corresponding divisor (10) when remainder equals 0 is taken as GCF.
What are the Methods to Find GCF of 10 and 70?
There are three commonly used methods to find the GCF of 10 and 70.
 By Prime Factorization
 By Listing Common Factors
 By Long Division
What is the Relation Between LCM and GCF of 10, 70?
The following equation can be used to express the relation between LCM and GCF of 10 and 70, i.e. GCF × LCM = 10 × 70.
If the GCF of 70 and 10 is 10, Find its LCM.
GCF(70, 10) × LCM(70, 10) = 70 × 10
Since the GCF of 70 and 10 = 10
⇒ 10 × LCM(70, 10) = 700
Therefore, LCM = 70
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