GCF of 10 and also 45 is the largest feasible number the divides 10 and also 45 precisely without any type of remainder. The determinants of 10 and 45 are 1, 2, 5, 10 and also 1, 3, 5, 9, 15, 45 respectively. There are 3 frequently used approaches to uncover the GCF that 10 and 45 - lengthy division, Euclidean algorithm, and also prime factorization.

You are watching: Greatest common factor of 10 and 45

1.GCF of 10 and 45
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF the 10 and 45 is 5.

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Explanation:

The GCF of 2 non-zero integers, x(10) and also y(45), is the greatest positive integer m(5) the divides both x(10) and y(45) without any remainder.


Let's look at the various methods because that finding the GCF of 10 and also 45.

Listing usual FactorsPrime administrate MethodLong department Method

GCF the 10 and also 45 by Listing common Factors

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Factors the 10: 1, 2, 5, 10Factors the 45: 1, 3, 5, 9, 15, 45

There are 2 common factors that 10 and also 45, that room 1 and 5. Therefore, the greatest common factor that 10 and 45 is 5.

GCF the 10 and 45 by element Factorization

Prime factorization of 10 and 45 is (2 × 5) and also (3 × 3 × 5) respectively. As visible, 10 and 45 have actually only one common prime element i.e. 5. Hence, the GCF that 10 and 45 is 5.

GCF of 10 and also 45 by lengthy Division

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GCF of 10 and 45 is the divisor the we get when the remainder becomes 0 after doing long division repeatedly.

Step 2: since the remainder ≠ 0, we will certainly divide the divisor of action 1 (10) by the remainder (5).Step 3: Repeat this process until the remainder = 0.

The matching divisor (5) is the GCF the 10 and 45.

☛ also Check:


GCF that 10 and also 45 Examples


Example 1: find the biggest number that divides 10 and 45 exactly.

Solution:

The best number the divides 10 and also 45 exactly is their greatest common factor, i.e. GCF of 10 and 45.⇒ factors of 10 and also 45:

Factors of 10 = 1, 2, 5, 10Factors of 45 = 1, 3, 5, 9, 15, 45

Therefore, the GCF the 10 and also 45 is 5.


Example 2: The product of 2 numbers is 450. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 450∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 450/5Therefore, the LCM is 90.


Example 3: uncover the GCF of 10 and also 45, if their LCM is 90.

Solution:

∵ LCM × GCF = 10 × 45⇒ GCF(10, 45) = (10 × 45)/90 = 5Therefore, the greatest common factor of 10 and 45 is 5.


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FAQs ~ above GCF that 10 and also 45

What is the GCF the 10 and also 45?

The GCF of 10 and 45 is 5. To calculation the GCF (Greatest typical Factor) of 10 and 45, we require to variable each number (factors of 10 = 1, 2, 5, 10; determinants of 45 = 1, 3, 5, 9, 15, 45) and choose the greatest factor that exactly divides both 10 and 45, i.e., 5.

If the GCF the 45 and also 10 is 5, uncover its LCM.

GCF(45, 10) × LCM(45, 10) = 45 × 10Since the GCF the 45 and 10 = 5⇒ 5 × LCM(45, 10) = 450Therefore, LCM = 90☛ GCF Calculator

What is the Relation between LCM and also GCF of 10, 45?

The following equation have the right to be provided to refer the relation in between Least common Multiple (LCM) and GCF of 10 and also 45, i.e. GCF × LCM = 10 × 45.

How to uncover the GCF that 10 and also 45 by prime Factorization?

To discover the GCF the 10 and also 45, we will find the element factorization of the offered numbers, i.e. 10 = 2 × 5; 45 = 3 × 3 × 5.⇒ since 5 is the only usual prime aspect of 10 and also 45. Hence, GCF (10, 45) = 5.☛ What is a element Number?

What space the approaches to find GCF the 10 and 45?

There room three frequently used techniques to uncover the GCF the 10 and 45.

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By long DivisionBy Euclidean AlgorithmBy element Factorization

How to uncover the GCF that 10 and 45 by Long division Method?

To discover the GCF the 10, 45 using long division method, 45 is divided by 10. The corresponding divisor (5) once remainder equals 0 is taken as GCF.