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

You are watching: Greatest common factor of 42 and 70

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

Answer: GCF the 42 and also 70 is 14.

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Explanation:

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


Let's look in ~ the various methods for finding the GCF the 42 and 70.

Listing usual FactorsPrime administrate MethodLong division Method

GCF the 42 and also 70 by Listing usual Factors

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

There are 4 common factors of 42 and also 70, that room 1, 2, 14, and 7. Therefore, the greatest usual factor that 42 and also 70 is 14.

GCF of 42 and 70 by element Factorization

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

GCF the 42 and also 70 by long Division

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GCF that 42 and 70 is the divisor the we obtain when the remainder becomes 0 after doing long division repeatedly.

Step 2: since the remainder ≠ 0, we will divide the divisor of step 1 (42) by the remainder (28).Step 3: Repeat this process until the remainder = 0.

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

☛ additionally Check:


GCF the 42 and 70 Examples


Example 1: discover the best number the divides 42 and 70 exactly.

Solution:

The greatest number that divides 42 and also 70 precisely is their greatest common factor, i.e. GCF that 42 and 70.⇒ components of 42 and also 70:

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

Therefore, the GCF the 42 and also 70 is 14.


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

Solution:

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


Example 3: find the GCF of 42 and 70, if their LCM is 210.

Solution:

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


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FAQs ~ above GCF the 42 and 70

What is the GCF the 42 and also 70?

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

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

The complying with equation have the right to be offered to express the relation between Least common Multiple (LCM) and GCF of 42 and 70, i.e. GCF × LCM = 42 × 70.

How to uncover the GCF of 42 and also 70 by Long department Method?

To discover the GCF of 42, 70 utilizing long department method, 70 is split by 42. The corresponding divisor (14) once remainder equates to 0 is taken as GCF.

How to uncover the GCF the 42 and also 70 by prime Factorization?

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

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

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

What are the methods to uncover GCF of 42 and 70?

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