GCF of 42 and 70 is the largest possible number the divides 42 and 70 specifically without any type of remainder. The factors of 42 and also 70 are 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 5, 7, 10, 14, 35, 70 respectively. There room 3 generally used techniques to uncover the GCF that 42 and 70 - long division, Euclidean algorithm, and prime factorization.

You are watching: What is the greatest common factor of 42 and 70

1.GCF of 42 and also 70
2.List the 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 y(70), is the best positive essence m(14) that divides both x(42) and also y(70) without any remainder.


Let's look at the different methods because that finding the GCF the 42 and also 70.

Listing typical FactorsPrime administer MethodLong division Method

GCF the 42 and also 70 by Listing common Factors

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

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

GCF the 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 70 have usual prime factors. Hence, the GCF that 42 and 70 is 2 × 7 = 14.

GCF of 42 and 70 by lengthy Division

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GCF the 42 and 70 is the divisor that we get when the remainder i do not care 0 ~ doing long division repeatedly.

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

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

☛ additionally Check:


GCF that 42 and 70 Examples


Example 1: uncover the greatest number that divides 42 and also 70 exactly.

Solution:

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

Factors that 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 2 numbers, GCF = 14 and LCM = 210. If one number is 70, uncover 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 that 42 and 70, if your LCM is 210.

Solution:

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


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FAQs ~ above GCF the 42 and also 70

What is the GCF of 42 and 70?

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

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

The complying with equation deserve to be used to refer the relation between Least typical Multiple (LCM) and also GCF of 42 and also 70, i.e. GCF × LCM = 42 × 70.

How to find the GCF the 42 and 70 by Long division Method?

To discover the GCF the 42, 70 utilizing long department method, 70 is divided by 42. The corresponding divisor (14) as soon as remainder equals 0 is taken as GCF.

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

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

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

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

What are the methods to discover GCF that 42 and also 70?

There are three typically used techniques to find the GCF of 42 and also 70.