GCF the 21 and 35 is the largest possible number that divides 21 and also 35 precisely without any type of remainder. The components of 21 and 35 are 1, 3, 7, 21 and 1, 5, 7, 35 respectively. There room 3 typically used techniques to find the GCF the 21 and 35 - prime factorization, lengthy division, and Euclidean algorithm.

You are watching: Greatest common factor of 21 and 35

1.GCF that 21 and also 35
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF that 21 and 35 is 7.

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Explanation:

The GCF of 2 non-zero integers, x(21) and y(35), is the biggest positive essence m(7) that divides both x(21) and also y(35) without any type of remainder.


Let's look at the various methods for finding the GCF that 21 and 35.

Long division MethodPrime factorization MethodListing common Factors

GCF that 21 and also 35 by long Division

GCF that 21 and 35 is the divisor the we gain 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 (21) by the remainder (14).Step 3: Repeat this procedure until the remainder = 0.

The matching divisor (7) is the GCF that 21 and also 35.

GCF that 21 and 35 by element Factorization

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Prime administrate of 21 and also 35 is (3 × 7) and also (5 × 7) respectively. As visible, 21 and 35 have only one typical prime variable i.e. 7. Hence, the GCF the 21 and also 35 is 7.

GCF that 21 and 35 by Listing common Factors

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Factors of 21: 1, 3, 7, 21Factors that 35: 1, 5, 7, 35

There are 2 usual factors the 21 and also 35, that room 1 and also 7. Therefore, the greatest common factor the 21 and 35 is 7.

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GCF of 21 and 35 Examples


Example 1: The product of 2 numbers is 735. If your GCF is 7, what is their LCM?

Solution:

Given: GCF = 7 and product of number = 735∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 735/7Therefore, the LCM is 105.


Example 2: For two numbers, GCF = 7 and LCM = 105. If one number is 21, find the various other number.

Solution:

Given: GCF (x, 21) = 7 and LCM (x, 21) = 105∵ GCF × LCM = 21 × (x)⇒ x = (GCF × LCM)/21⇒ x = (7 × 105)/21⇒ x = 35Therefore, the various other number is 35.


Example 3: find the GCF that 21 and also 35, if their LCM is 105.

Solution:

∵ LCM × GCF = 21 × 35⇒ GCF(21, 35) = (21 × 35)/105 = 7Therefore, the greatest usual factor that 21 and also 35 is 7.


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FAQs on GCF of 21 and 35

What is the GCF the 21 and 35?

The GCF that 21 and also 35 is 7. To calculate the greatest typical factor (GCF) that 21 and 35, we require to element each number (factors the 21 = 1, 3, 7, 21; determinants of 35 = 1, 5, 7, 35) and also choose the greatest variable that specifically divides both 21 and 35, i.e., 7.

What are the techniques to find GCF that 21 and also 35?

There are three commonly used methods to uncover the GCF that 21 and also 35.

By long DivisionBy Listing usual FactorsBy element Factorization

How to uncover the GCF the 21 and 35 by Long division Method?

To uncover the GCF the 21, 35 utilizing long department method, 35 is split by 21. The equivalent divisor (7) once remainder amounts to 0 is taken as GCF.

What is the Relation between LCM and GCF of 21, 35?

The following equation have the right to be provided to to express the relation between Least usual Multiple and also GCF the 21 and 35, i.e. GCF × LCM = 21 × 35.

See more: Why Did Researchers Originally Think That Protein Was The Genetic Material ?

If the GCF the 35 and also 21 is 7, uncover its LCM.

GCF(35, 21) × LCM(35, 21) = 35 × 21Since the GCF of 35 and also 21 = 7⇒ 7 × LCM(35, 21) = 735Therefore, LCM = 105☛ GCF Calculator

How to find the GCF that 21 and 35 by element Factorization?

To discover the GCF of 21 and 35, we will uncover the element factorization the the offered numbers, i.e. 21 = 3 × 7; 35 = 5 × 7.⇒ since 7 is the only usual prime aspect of 21 and 35. Hence, GCF (21, 35) = 7.☛ What space Prime Numbers?