GCF the 42 and 70 is the largest feasible number the divides 42 and 70 specifically without any kind of remainder. The determinants of 42 and also 70 space 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 5, 7, 10, 14, 35, 70 respectively. There space 3 typically used approaches to discover the GCF that 42 and also 70 - lengthy division, Euclidean algorithm, and also prime factorization.

You are watching: What is the gcf of 42 and 70

1.GCF that 42 and also 70
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF the 42 and 70 is 14.

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Explanation:

The GCF of 2 non-zero integers, x(42) and also y(70), is the best positive creature m(14) the divides both x(42) and also y(70) without any kind of remainder.


Let's look at the various methods for finding the GCF of 42 and also 70.

Listing usual FactorsPrime administer MethodLong division Method

GCF of 42 and also 70 through Listing typical Factors

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Factors the 42: 1, 2, 3, 6, 7, 14, 21, 42Factors that 70: 1, 2, 5, 7, 10, 14, 35, 70

There space 4 typical factors the 42 and 70, that are 1, 2, 14, and also 7. Therefore, the greatest typical factor the 42 and also 70 is 14.

GCF of 42 and 70 by element Factorization

Prime administrate of 42 and also 70 is (2 × 3 × 7) and also (2 × 5 × 7) respectively. Together visible, 42 and also 70 have common prime factors. Hence, the GCF the 42 and 70 is 2 × 7 = 14.

GCF of 42 and also 70 by lengthy Division

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GCF the 42 and also 70 is the divisor that we obtain when the remainder becomes 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 (42) through the remainder (28).Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (14) is the GCF that 42 and also 70.

☛ additionally Check:


GCF of 42 and 70 Examples


Example 1: find the biggest number that divides 42 and 70 exactly.

Solution:

The biggest number that divides 42 and 70 precisely is your greatest usual factor, i.e. GCF that 42 and 70.⇒ factors of 42 and 70:

Factors the 42 = 1, 2, 3, 6, 7, 14, 21, 42Factors that 70 = 1, 2, 5, 7, 10, 14, 35, 70

Therefore, the GCF the 42 and 70 is 14.


Example 2: For 2 numbers, GCF = 14 and also LCM = 210. If one number is 70, find the other number.

Solution:

Given: GCF (y, 70) = 14 and also LCM (y, 70) = 210∵ GCF × LCM = 70 × (y)⇒ y = (GCF × LCM)/70⇒ y = (14 × 210)/70⇒ y = 42Therefore, the other number is 42.


Example 3: discover the GCF that 42 and also 70, if your LCM is 210.

Solution:

∵ LCM × GCF = 42 × 70⇒ GCF(42, 70) = (42 × 70)/210 = 14Therefore, the greatest typical factor that 42 and also 70 is 14.


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FAQs top top GCF that 42 and also 70

What is the GCF that 42 and also 70?

The GCF that 42 and 70 is 14. To calculate the GCF of 42 and also 70, we need to aspect each number (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; components of 70 = 1, 2, 5, 7, 10, 14, 35, 70) and choose the greatest factor that precisely divides both 42 and 70, i.e., 14.

What is the Relation between LCM and also GCF of 42, 70?

The following equation have the right to be supplied to refer the relation in between Least common Multiple (LCM) and also GCF of 42 and 70, i.e. GCF × LCM = 42 × 70.

How to discover the GCF that 42 and also 70 by Long division Method?

To uncover the GCF that 42, 70 using long department method, 70 is split by 42. The equivalent divisor (14) as soon as remainder amounts to 0 is taken together GCF.

How to discover the GCF the 42 and 70 by element Factorization?

To discover the GCF of 42 and 70, we will discover the element factorization that the offered numbers, i.e. 42 = 2 × 3 × 7; 70 = 2 × 5 × 7.⇒ because 2, 7 are usual terms in the element factorization the 42 and 70. Hence, GCF(42, 70) = 2 × 7 = 14☛ What is a element Number?

If the GCF of 70 and also 42 is 14, discover its LCM.

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GCF(70, 42) × LCM(70, 42) = 70 × 42Since the GCF that 70 and 42 = 14⇒ 14 × LCM(70, 42) = 2940Therefore, LCM = 210☛ GCF Calculator

What are the approaches to discover GCF of 42 and 70?

There room three generally used techniques to find the GCF the 42 and also 70.