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GCF of 27 and 70

GCF of 27 and 70 is the largest possible number that divides 27 and 70 exactly without any remainder. The factors of 27 and 70 are 1, 3, 9, 27 and 1, 2, 5, 7, 10, 14, 35, 70 respectively. There are 3 commonly used methods to find the GCF of 27 and 70 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 27 and 70
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 27 and 70?

Answer: GCF of 27 and 70 is 1.

Explanation:

The GCF of two non-zero integers, x(27) and y(70), is the greatest positive integer m(1) that divides both x(27) and y(70) without any remainder.

Methods to Find GCF of 27 and 70

The methods to find the GCF of 27 and 70 are explained below.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 27 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 = 27

GCF(70, 27) = GCF(27, 70 mod 27) = GCF(27, 16)
GCF(27, 16) = GCF(16, 27 mod 16) = GCF(16, 11)
GCF(16, 11) = GCF(11, 16 mod 11) = GCF(11, 5)
GCF(11, 5) = GCF(5, 11 mod 5) = GCF(5, 1)
GCF(5, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 27 and 70 is 1.

GCF of 27 and 70 by Long Division

GCF of 27 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 27 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (27) by the remainder (16).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 27 and 70.

GCF of 27 and 70 by Prime Factorization

Prime factorization of 27 and 70 is (3 × 3 × 3) and (2 × 5 × 7) respectively. As visible, there are no common prime factors between 27 and 70, i.e. they are co-prime. Hence, the GCF of 27 and 70 will be 1.

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GCF of 27 and 70 Examples

Example 1: For two numbers, GCF = 1 and LCM = 1890. If one number is 70, find the other number.

Solution:

Given: GCF (x, 70) = 1 and LCM (x, 70) = 1890
∵ GCF × LCM = 70 × (x)
⇒ x = (GCF × LCM)/70
⇒ x = (1 × 1890)/70
⇒ x = 27
Therefore, the other number is 27.
Example 2: Find the greatest number that divides 27 and 70 exactly.

Solution:

The greatest number that divides 27 and 70 exactly is their greatest common factor, i.e. GCF of 27 and 70.
⇒ Factors of 27 and 70:
- Factors of 27 = 1, 3, 9, 27
- Factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70
Therefore, the GCF of 27 and 70 is 1.
Example 3: Find the GCF of 27 and 70, if their LCM is 1890.

Solution:

∵ LCM × GCF = 27 × 70
⇒ GCF(27, 70) = (27 × 70)/1890 = 1
Therefore, the greatest common factor of 27 and 70 is 1.

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FAQs on GCF of 27 and 70

What is the GCF of 27 and 70?

The GCF of 27 and 70 is 1. To calculate the GCF (Greatest Common Factor) of 27 and 70, we need to factor each number (factors of 27 = 1, 3, 9, 27; factors of 70 = 1, 2, 5, 7, 10, 14, 35, 70) and choose the greatest factor that exactly divides both 27 and 70, i.e., 1.

If the GCF of 70 and 27 is 1, Find its LCM.

GCF(70, 27) × LCM(70, 27) = 70 × 27
Since the GCF of 70 and 27 = 1
⇒ 1 × LCM(70, 27) = 1890
Therefore, LCM = 1890
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How to Find the GCF of 27 and 70 by Prime Factorization?

To find the GCF of 27 and 70, we will find the prime factorization of the given numbers, i.e. 27 = 3 × 3 × 3; 70 = 2 × 5 × 7.
⇒ There is no common prime factor for 27 and 70. Hence, GCF (27, 70) = 1.
☛ Prime Number

How to Find the GCF of 27 and 70 by Long Division Method?

To find the GCF of 27, 70 using long division method, 70 is divided by 27. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 27, 70?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 27 and 70, i.e. GCF × LCM = 27 × 70.

What are the Methods to Find GCF of 27 and 70?

There are three commonly used methods to find the GCF of 27 and 70.

By Long Division
By Prime Factorization
By Listing Common Factors

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