GCF the 30 and also 70 is the largest possible number that divides 30 and also 70 specifically without any kind of remainder. The determinants of 30 and also 70 are 1, 2, 3, 5, 6, 10, 15, 30 and also 1, 2, 5, 7, 10, 14, 35, 70 respectively. There space 3 frequently used techniques to find the GCF that 30 and 70 - lengthy division, element factorization, and also Euclidean algorithm.

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

Answer: GCF that 30 and 70 is 10.

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Explanation:

The GCF of two non-zero integers, x(30) and also y(70), is the biggest positive creature m(10) the divides both x(30) and also y(70) without any kind of remainder.


The approaches to uncover the GCF the 30 and also 70 are described below.

Listing common FactorsLong department MethodPrime factorization Method

GCF of 30 and 70 by Listing common Factors

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

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

GCF the 30 and also 70 by lengthy Division

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GCF of 30 and also 70 is the divisor that we get when the remainder i do not care 0 after ~ doing long division repeatedly.

Step 2: due to the fact that the remainder ≠ 0, we will certainly divide the divisor of step 1 (30) by the remainder (10).Step 3: Repeat this procedure until the remainder = 0.

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

GCF that 30 and 70 by element Factorization

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

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GCF the 30 and 70 Examples


Example 1: discover the biggest number that divides 30 and 70 exactly.

Solution:

The biggest number the divides 30 and 70 precisely is your greatest usual factor, i.e. GCF the 30 and 70.⇒ components of 30 and 70:

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

Therefore, the GCF the 30 and 70 is 10.


Example 2: For 2 numbers, GCF = 10 and also LCM = 210. If one number is 30, discover the other number.

Solution:

Given: GCF (x, 30) = 10 and also LCM (x, 30) = 210∵ GCF × LCM = 30 × (x)⇒ x = (GCF × LCM)/30⇒ x = (10 × 210)/30⇒ x = 70Therefore, 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 also product of number = 2100∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 2100/10Therefore, the LCM is 210.


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FAQs on GCF the 30 and 70

What is the GCF the 30 and also 70?

The GCF the 30 and also 70 is 10. To calculate the greatest usual factor that 30 and 70, we require to aspect each number (factors that 30 = 1, 2, 3, 5, 6, 10, 15, 30; determinants of 70 = 1, 2, 5, 7, 10, 14, 35, 70) and also choose the greatest element that specifically divides both 30 and also 70, i.e., 10.

What room the approaches to uncover GCF of 30 and 70?

There are three typically used methods to discover the GCF that 30 and 70.

By long DivisionBy element FactorizationBy Listing typical Factors

What is the Relation between LCM and also GCF the 30, 70?

The complying with equation can be provided to to express the relation between Least typical Multiple and GCF the 30 and 70, i.e. GCF × LCM = 30 × 70.

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

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GCF(70, 30) × LCM(70, 30) = 70 × 30Since the GCF of 70 and also 30 = 10⇒ 10 × LCM(70, 30) = 2100Therefore, LCM = 210☛ Greatest usual Factor Calculator

How to discover the GCF the 30 and 70 by prime Factorization?

To uncover the GCF of 30 and also 70, us will discover the prime factorization of the provided numbers, i.e. 30 = 2 × 3 × 5; 70 = 2 × 5 × 7.⇒ because 2, 5 are typical terms in the prime factorization the 30 and also 70. Hence, GCF(30, 70) = 2 × 5 = 10☛ What room Prime Numbers?

How to discover the GCF the 30 and also 70 through Long department Method?

To uncover the GCF the 30, 70 utilizing long division method, 70 is split by 30. The corresponding divisor (10) as soon as remainder equals 0 is taken as GCF.