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GCF of 30 and 70

GCF of 30 and 70 is the largest possible number that divides 30 and 70 exactly without any remainder. The factors of 30 and 70 are 1, 2, 3, 5, 6, 10, 15, 30 and 1, 2, 5, 7, 10, 14, 35, 70 respectively. There are 3 commonly used methods to find the GCF of 30 and 70 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 30 and 70
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 30 and 70?

Answer: GCF of 30 and 70 is 10.

Explanation:

The GCF of two non-zero integers, x(30) and y(70), is the greatest positive integer m(10) that divides both x(30) and y(70) without any remainder.

Methods to Find GCF of 30 and 70

The methods to find the GCF of 30 and 70 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 30 and 70 by Listing Common Factors

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70

There are 4 common factors of 30 and 70, that are 1, 2, 10, and 5. Therefore, the greatest common factor of 30 and 70 is 10.

GCF of 30 and 70 by Long Division

GCF of 30 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 30 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (30) by the remainder (10).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (10) is the GCF of 30 and 70.

GCF of 30 and 70 by Prime Factorization

Prime factorization of 30 and 70 is (2 × 3 × 5) and (2 × 5 × 7) respectively. As visible, 30 and 70 have common prime factors. Hence, the GCF of 30 and 70 is 2 × 5 = 10.

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GCF of 30 and 70 Examples

Example 1: Find the greatest number that divides 30 and 70 exactly.

Solution:

The greatest number that divides 30 and 70 exactly is their greatest common factor, i.e. GCF of 30 and 70.
⇒ Factors of 30 and 70:
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70
Therefore, the GCF of 30 and 70 is 10.
Example 2: For two numbers, GCF = 10 and LCM = 210. If one number is 30, find the other number.

Solution:

Given: GCF (x, 30) = 10 and LCM (x, 30) = 210
∵ GCF × LCM = 30 × (x)
⇒ x = (GCF × LCM)/30
⇒ x = (10 × 210)/30
⇒ x = 70
Therefore, the other number is 70.
Example 3: The product of two numbers is 2100. If their GCF is 10, what is their LCM?

Solution:

Given: GCF = 10 and product of numbers = 2100
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2100/10
Therefore, the LCM is 210.

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FAQs on GCF of 30 and 70

What is the GCF of 30 and 70?

The GCF of 30 and 70 is 10. To calculate the greatest common factor of 30 and 70, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70) and choose the greatest factor that exactly divides both 30 and 70, i.e., 10.

What are the Methods to Find GCF of 30 and 70?

There are three commonly used methods to find the GCF of 30 and 70.

By Long Division
By Prime Factorization
By Listing Common Factors

What is the Relation Between LCM and GCF of 30, 70?

The following equation can be used to express the relation between Least Common Multiple and GCF of 30 and 70, i.e. GCF × LCM = 30 × 70.

If the GCF of 70 and 30 is 10, Find its LCM.

GCF(70, 30) × LCM(70, 30) = 70 × 30
Since the GCF of 70 and 30 = 10
⇒ 10 × LCM(70, 30) = 2100
Therefore, LCM = 210
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How to Find the GCF of 30 and 70 by Prime Factorization?

To find the GCF of 30 and 70, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 70 = 2 × 5 × 7.
⇒ Since 2, 5 are common terms in the prime factorization of 30 and 70. Hence, GCF(30, 70) = 2 × 5 = 10
☛ What are Prime Numbers?

How to Find the GCF of 30 and 70 by Long Division Method?

To find the GCF of 30, 70 using long division method, 70 is divided by 30. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

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