GCF of 42 and 70 is the largest possible number the divides 42 and also 70 precisely without any type of remainder. The factors of 42 and 70 space 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 5, 7, 10, 14, 35, 70 respectively. There room 3 commonly used methods to discover the GCF of 42 and also 70 - lengthy division, Euclidean algorithm, and prime factorization.

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

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

Answer: GCF of 42 and 70 is 14.

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Explanation:

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


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

Listing typical FactorsPrime administer MethodLong department Method

GCF that 42 and 70 by Listing usual 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 common factors the 42 and 70, that space 1, 2, 14, and also 7. Therefore, the greatest typical factor of 42 and 70 is 14.

GCF of 42 and also 70 by element Factorization

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

GCF that 42 and also 70 by long Division

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GCF of 42 and also 70 is the divisor that we get when the remainder becomes 0 after ~ doing long department repeatedly.

Step 2: due to the fact that 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 also 70 Examples


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

Solution:

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

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

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


Example 2: For two numbers, GCF = 14 and LCM = 210. If one number is 70, uncover 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 various other number is 42.


Example 3: find the GCF the 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 the 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 the 42 and 70 is 14. To calculate the GCF of 42 and also 70, we require to element each number (factors the 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 exactly divides both 42 and 70, i.e., 14.

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

The adhering to equation can be used to to express the relation between Least common Multiple (LCM) and GCF of 42 and also 70, i.e. GCF × LCM = 42 × 70.

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

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

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

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

If the GCF of 70 and also 42 is 14, find 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 room the methods to uncover GCF the 42 and also 70?

There are three commonly used approaches to uncover the GCF the 42 and 70.