How to find factors of 30 using prime factorization / Prime factors of 30 / #shorts / #ncertmath
How to find factors of 30 using prime factorization / Prime factors of 30 / #shorts / #ncertmath

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GCF of 30 and 40

GCF of 30 and 40 is the largest possible number that divides 30 and 40 exactly without any remainder. The factors of 30 and 40 are 1, 2, 3, 5, 6, 10, 15, 30 and 1, 2, 4, 5, 8, 10, 20, 40 respectively. There are 3 commonly used methods to find the GCF of 30 and 40 – long division, prime factorization, and Euclidean algorithm.

1. GCF of 30 and 40
2. List of Methods
3. Solved Examples
4. FAQs

What is GCF of 30 and 40?

Answer: GCF of 30 and 40 is 10.

GCF of 30 and 40

Explanation:

The GCF of two non-zero integers, x(30) and y(40), is the greatest positive integer m(10) that divides both x(30) and y(40) without any remainder.

Methods to Find GCF of 30 and 40

Let’s look at the different methods for finding the GCF of 30 and 40.

  • Prime Factorization Method
  • Using Euclid’s Algorithm
  • Listing Common Factors

GCF of 30 and 40 by Prime Factorization

GCF of 30 and 40 by Prime Factorization

Prime factorization of 30 and 40 is (2 × 3 × 5) and (2 × 2 × 2 × 5) respectively. As visible, 30 and 40 have common prime factors. Hence, the GCF of 30 and 40 is 2 × 5 = 10.

GCF of 30 and 40 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 40 and Y = 30

  • GCF(40, 30) = GCF(30, 40 mod 30) = GCF(30, 10)
  • GCF(30, 10) = GCF(10, 30 mod 10) = GCF(10, 0)
  • GCF(10, 0) = 10 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 30 and 40 is 10.

GCF of 30 and 40 by Listing Common Factors

GCF of 30 and 40 by Listing Common Factors

  • Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
  • Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

There are 4 common factors of 30 and 40, that are 1, 2, 10, and 5. Therefore, the greatest common factor of 30 and 40 is 10.

☛ Also Check:

  • GCF of 18 and 21 = 3
  • GCF of 54 and 27 = 27
  • GCF of 42 and 90 = 6
  • GCF of 9 and 21 = 3
  • GCF of 15 and 21 = 3
  • GCF of 86 and 42 = 2
  • GCF of 14 and 49 = 7

GCF of 30 and 40 Examples

  1. Example 1: Find the GCF of 30 and 40, if their LCM is 120.

    Solution:

    ∵ LCM × GCF = 30 × 40

    ⇒ GCF(30, 40) = (30 × 40)/120 = 10
    Therefore, the greatest common factor of 30 and 40 is 10.

  2. Example 2: For two numbers, GCF = 10 and LCM = 120. If one number is 30, find the other number.

    Solution:

    Given: GCF (z, 30) = 10 and LCM (z, 30) = 120

    ∵ GCF × LCM = 30 × (z)
    ⇒ z = (GCF × LCM)/30
    ⇒ z = (10 × 120)/30
    ⇒ z = 40
    Therefore, the other number is 40.

  3. Example 3: Find the greatest number that divides 30 and 40 exactly.

    Solution:

    The greatest number that divides 30 and 40 exactly is their greatest common factor, i.e. GCF of 30 and 40.

    ⇒ Factors of 30 and 40:

    • Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
    • Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40

    Therefore, the GCF of 30 and 40 is 10.

FAQs on GCF of 30 and 40

What is the GCF of 30 and 40?

The GCF of 30 and 40 is 10. To calculate the greatest common factor (GCF) of 30 and 40, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the greatest factor that exactly divides both 30 and 40, i.e., 10.

How to Find the GCF of 30 and 40 by Prime Factorization?

To find the GCF of 30 and 40, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 40 = 2 × 2 × 2 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 30 and 40. Hence, GCF(30, 40) = 2 × 5 = 10
☛ Prime Number

What is the Relation Between LCM and GCF of 30, 40?

The following equation can be used to express the relation between LCM and GCF of 30 and 40, i.e. GCF × LCM = 30 × 40.

How to Find the GCF of 30 and 40 by Long Division Method?

To find the GCF of 30, 40 using long division method, 40 is divided by 30. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

If the GCF of 40 and 30 is 10, Find its LCM.

GCF(40, 30) × LCM(40, 30) = 40 × 30
Since the GCF of 40 and 30 = 10
⇒ 10 × LCM(40, 30) = 1200
Therefore, LCM = 120
☛ GCF Calculator

What are the Methods to Find GCF of 30 and 40?

There are three commonly used methods to find the GCF of 30 and 40.

  • By Euclidean Algorithm
  • By Prime Factorization
  • By Long Division

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