GCF of 42 and 70
GCF of 42 and 70 is the largest possible number that divides 42 and 70 exactly without any remainder. The factors of 42 and 70 are 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 5, 7, 10, 14, 35, 70 respectively. There are 3 commonly used methods to find the GCF of 42 and 70 - long division, Euclidean algorithm, and prime factorization.
| 1. | GCF of 42 and 70 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 42 and 70?
Answer: GCF of 42 and 70 is 14.
Explanation:
The GCF of two non-zero integers, x(42) and y(70), is the greatest positive integer m(14) that divides both x(42) and y(70) without any remainder.
Methods to Find GCF of 42 and 70
Let's look at the different methods for finding the GCF of 42 and 70.
- Listing Common Factors
- Prime Factorization Method
- Long Division Method
GCF of 42 and 70 by Listing Common Factors
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
There are 4 common factors of 42 and 70, that are 1, 2, 14, and 7. Therefore, the greatest common factor of 42 and 70 is 14.
GCF of 42 and 70 by Prime Factorization
Prime factorization of 42 and 70 is (2 × 3 × 7) and (2 × 5 × 7) respectively. As visible, 42 and 70 have common prime factors. Hence, the GCF of 42 and 70 is 2 × 7 = 14.
GCF of 42 and 70 by Long Division
GCF of 42 and 70 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 70 (larger number) by 42 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (42) by the remainder (28).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (14) is the GCF of 42 and 70.
☛ Also Check:
- GCF of 30 and 45 = 15
- GCF of 36 and 81 = 9
- GCF of 3 and 7 = 1
- GCF of 81 and 108 = 27
- GCF of 18 and 81 = 9
- GCF of 40 and 48 = 8
- GCF of 17 and 51 = 17
FAQs on GCF of 42 and 70
What is the GCF of 42 and 70?
The GCF of 42 and 70 is 14. To calculate the GCF of 42 and 70, we need to factor each number (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors 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 Between LCM and GCF of 42, 70?
The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 42 and 70, i.e. GCF × LCM = 42 × 70.
How to Find the GCF of 42 and 70 by Long Division Method?
To find the GCF of 42, 70 using long division method, 70 is divided by 42. The corresponding divisor (14) when remainder equals 0 is taken as GCF.
How to Find the GCF of 42 and 70 by Prime Factorization?
To find the GCF of 42 and 70, we will find the prime factorization of the given numbers, i.e. 42 = 2 × 3 × 7; 70 = 2 × 5 × 7.
⇒ Since 2, 7 are common terms in the prime factorization of 42 and 70. Hence, GCF(42, 70) = 2 × 7 = 14
☛ What is a Prime Number?
If the GCF of 70 and 42 is 14, Find its LCM.
GCF(70, 42) × LCM(70, 42) = 70 × 42
Since the GCF of 70 and 42 = 14
⇒ 14 × LCM(70, 42) = 2940
Therefore, LCM = 210
☛ GCF Calculator
What are the Methods to Find GCF of 42 and 70?
There are three commonly used methods to find the GCF of 42 and 70.
- By Prime Factorization
- By Listing Common Factors
- By Long Division