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GCF of 10 and 35

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

1.	GCF of 10 and 35
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 10 and 35?

Answer: GCF of 10 and 35 is 5.

Explanation:

The GCF of two non-zero integers, x(10) and y(35), is the greatest positive integer m(5) that divides both x(10) and y(35) without any remainder.

Methods to Find GCF of 10 and 35

The methods to find the GCF of 10 and 35 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

GCF of 10 and 35 by Prime Factorization

Prime factorization of 10 and 35 is (2 × 5) and (5 × 7) respectively. As visible, 10 and 35 have only one common prime factor i.e. 5. Hence, the GCF of 10 and 35 is 5.

GCF of 10 and 35 by Long Division

GCF of 10 and 35 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 35 (larger number) by 10 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (10) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 10 and 35.

GCF of 10 and 35 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 = 35 and Y = 10

GCF(35, 10) = GCF(10, 35 mod 10) = GCF(10, 5)
GCF(10, 5) = GCF(5, 10 mod 5) = GCF(5, 0)
GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 10 and 35 is 5.

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GCF of 10 and 35 Examples

Example 1: Find the GCF of 10 and 35, if their LCM is 70.

Solution:

∵ LCM × GCF = 10 × 35
⇒ GCF(10, 35) = (10 × 35)/70 = 5
Therefore, the greatest common factor of 10 and 35 is 5.
Example 2: Find the greatest number that divides 10 and 35 exactly.

Solution:

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

Solution:

Given: GCF (z, 10) = 5 and LCM (z, 10) = 70
∵ GCF × LCM = 10 × (z)
⇒ z = (GCF × LCM)/10
⇒ z = (5 × 70)/10
⇒ z = 35
Therefore, the other number is 35.

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FAQs on GCF of 10 and 35

What is the GCF of 10 and 35?

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

What are the Methods to Find GCF of 10 and 35?

There are three commonly used methods to find the GCF of 10 and 35.

By Prime Factorization
By Listing Common Factors
By Long Division

If the GCF of 35 and 10 is 5, Find its LCM.

GCF(35, 10) × LCM(35, 10) = 35 × 10
Since the GCF of 35 and 10 = 5
⇒ 5 × LCM(35, 10) = 350
Therefore, LCM = 70
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What is the Relation Between LCM and GCF of 10, 35?

The following equation can be used to express the relation between Least Common Multiple and GCF of 10 and 35, i.e. GCF × LCM = 10 × 35.

How to Find the GCF of 10 and 35 by Long Division Method?

To find the GCF of 10, 35 using long division method, 35 is divided by 10. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

How to Find the GCF of 10 and 35 by Prime Factorization?

To find the GCF of 10 and 35, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 35 = 5 × 7.
⇒ Since 5 is the only common prime factor of 10 and 35. Hence, GCF (10, 35) = 5.
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