GCF of 42 and 98
GCF of 42 and 98 is the largest possible number that divides 42 and 98 exactly without any remainder. The factors of 42 and 98 are 1, 2, 3, 6, 7, 14, 21, 42 and 1, 2, 7, 14, 49, 98 respectively. There are 3 commonly used methods to find the GCF of 42 and 98 - prime factorization, Euclidean algorithm, and long division.
| 1. | GCF of 42 and 98 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 42 and 98?
Answer: GCF of 42 and 98 is 14.
Explanation:
The GCF of two non-zero integers, x(42) and y(98), is the greatest positive integer m(14) that divides both x(42) and y(98) without any remainder.
Methods to Find GCF of 42 and 98
The methods to find the GCF of 42 and 98 are explained below.
- Long Division Method
- Prime Factorization Method
- Using Euclid's Algorithm
GCF of 42 and 98 by Long Division
GCF of 42 and 98 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 98 (larger number) by 42 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (42) by the remainder (14).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (14) is the GCF of 42 and 98.
GCF of 42 and 98 by Prime Factorization
Prime factorization of 42 and 98 is (2 × 3 × 7) and (2 × 7 × 7) respectively. As visible, 42 and 98 have common prime factors. Hence, the GCF of 42 and 98 is 2 × 7 = 14.
GCF of 42 and 98 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 = 98 and Y = 42
- GCF(98, 42) = GCF(42, 98 mod 42) = GCF(42, 14)
- GCF(42, 14) = GCF(14, 42 mod 14) = GCF(14, 0)
- GCF(14, 0) = 14 (∵ GCF(X, 0) = |X|, where X ≠ 0)
Therefore, the value of GCF of 42 and 98 is 14.
☛ Also Check:
- GCF of 22 and 33 = 11
- GCF of 22 and 44 = 22
- GCF of 45 and 105 = 15
- GCF of 39 and 6 = 3
- GCF of 6 and 7 = 1
- GCF of 21 and 36 = 3
- GCF of 72 and 84 = 12
FAQs on GCF of 42 and 98
What is the GCF of 42 and 98?
The GCF of 42 and 98 is 14. To calculate the GCF of 42 and 98, we need to factor each number (factors of 42 = 1, 2, 3, 6, 7, 14, 21, 42; factors of 98 = 1, 2, 7, 14, 49, 98) and choose the greatest factor that exactly divides both 42 and 98, i.e., 14.
How to Find the GCF of 42 and 98 by Long Division Method?
To find the GCF of 42, 98 using long division method, 98 is divided by 42. The corresponding divisor (14) when remainder equals 0 is taken as GCF.
How to Find the GCF of 42 and 98 by Prime Factorization?
To find the GCF of 42 and 98, we will find the prime factorization of the given numbers, i.e. 42 = 2 × 3 × 7; 98 = 2 × 7 × 7.
⇒ Since 2, 7 are common terms in the prime factorization of 42 and 98. Hence, GCF(42, 98) = 2 × 7 = 14
☛ What is a Prime Number?
What are the Methods to Find GCF of 42 and 98?
There are three commonly used methods to find the GCF of 42 and 98.
- By Long Division
- By Listing Common Factors
- By Prime Factorization
If the GCF of 98 and 42 is 14, Find its LCM.
GCF(98, 42) × LCM(98, 42) = 98 × 42
Since the GCF of 98 and 42 = 14
⇒ 14 × LCM(98, 42) = 4116
Therefore, LCM = 294
☛ Greatest Common Factor Calculator
What is the Relation Between LCM and GCF of 42, 98?
The following equation can be used to express the relation between Least Common Multiple and GCF of 42 and 98, i.e. GCF × LCM = 42 × 98.