GCF of 30 and 42
GCF of 30 and 42 is the largest possible number that divides 30 and 42 exactly without any remainder. The factors of 30 and 42 are 1, 2, 3, 5, 6, 10, 15, 30 and 1, 2, 3, 6, 7, 14, 21, 42 respectively. There are 3 commonly used methods to find the GCF of 30 and 42 - prime factorization, long division, and Euclidean algorithm.
| 1. | GCF of 30 and 42 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 30 and 42?
Answer: GCF of 30 and 42 is 6.
Explanation:
The GCF of two non-zero integers, x(30) and y(42), is the greatest positive integer m(6) that divides both x(30) and y(42) without any remainder.
Methods to Find GCF of 30 and 42
Let's look at the different methods for finding the GCF of 30 and 42.
- Listing Common Factors
- Long Division Method
- Prime Factorization Method
GCF of 30 and 42 by Listing Common Factors
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
There are 4 common factors of 30 and 42, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 30 and 42 is 6.
GCF of 30 and 42 by Long Division
GCF of 30 and 42 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 42 (larger number) by 30 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (30) by the remainder (12).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (6) is the GCF of 30 and 42.
GCF of 30 and 42 by Prime Factorization
Prime factorization of 30 and 42 is (2 × 3 × 5) and (2 × 3 × 7) respectively. As visible, 30 and 42 have common prime factors. Hence, the GCF of 30 and 42 is 2 × 3 = 6.
☛ Also Check:
- GCF of 7 and 28 = 7
- GCF of 64 and 144 = 16
- GCF of 75 and 125 = 25
- GCF of 25 and 60 = 5
- GCF of 24 and 56 = 8
- GCF of 21 and 28 = 7
- GCF of 30 and 50 = 10
FAQs on GCF of 30 and 42
What is the GCF of 30 and 42?
The GCF of 30 and 42 is 6. To calculate the greatest common factor of 30 and 42, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42) and choose the greatest factor that exactly divides both 30 and 42, i.e., 6.
How to Find the GCF of 30 and 42 by Long Division Method?
To find the GCF of 30, 42 using long division method, 42 is divided by 30. The corresponding divisor (6) when remainder equals 0 is taken as GCF.
How to Find the GCF of 30 and 42 by Prime Factorization?
To find the GCF of 30 and 42, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 42 = 2 × 3 × 7.
⇒ Since 2, 3 are common terms in the prime factorization of 30 and 42. Hence, GCF(30, 42) = 2 × 3 = 6
☛ Prime Number
If the GCF of 42 and 30 is 6, Find its LCM.
GCF(42, 30) × LCM(42, 30) = 42 × 30
Since the GCF of 42 and 30 = 6
⇒ 6 × LCM(42, 30) = 1260
Therefore, LCM = 210
☛ Greatest Common Factor Calculator
What is the Relation Between LCM and GCF of 30, 42?
The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 30 and 42, i.e. GCF × LCM = 30 × 42.
What are the Methods to Find GCF of 30 and 42?
There are three commonly used methods to find the GCF of 30 and 42.
- By Euclidean Algorithm
- By Long Division
- By Prime Factorization