GCF of 18 and 35
GCF of 18 and 35 is the largest possible number that divides 18 and 35 exactly without any remainder. The factors of 18 and 35 are 1, 2, 3, 6, 9, 18 and 1, 5, 7, 35 respectively. There are 3 commonly used methods to find the GCF of 18 and 35 - long division, prime factorization, and Euclidean algorithm.
| 1. | GCF of 18 and 35 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is GCF of 18 and 35?
Answer: GCF of 18 and 35 is 1.
Explanation:
The GCF of two non-zero integers, x(18) and y(35), is the greatest positive integer m(1) that divides both x(18) and y(35) without any remainder.
Methods to Find GCF of 18 and 35
Let's look at the different methods for finding the GCF of 18 and 35.
- Long Division Method
- Prime Factorization Method
- Listing Common Factors
GCF of 18 and 35 by Long Division
GCF of 18 and 35 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 35 (larger number) by 18 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (17).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (1) is the GCF of 18 and 35.
GCF of 18 and 35 by Prime Factorization
Prime factorization of 18 and 35 is (2 × 3 × 3) and (5 × 7) respectively. As visible, there are no common prime factors between 18 and 35, i.e. they are coprime. Hence, the GCF of 18 and 35 will be 1.
GCF of 18 and 35 by Listing Common Factors
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 35: 1, 5, 7, 35
Since, 1 is the only common factor between 18 and 35. The Greatest Common Factor of 18 and 35 is 1.
☛ Also Check:
- GCF of 28 and 40 = 4
- GCF of 8 and 40 = 8
- GCF of 40 and 56 = 8
- GCF of 20 and 36 = 4
- GCF of 60 and 72 = 12
- GCF of 50 and 60 = 10
- GCF of 12 and 28 = 4
FAQs on GCF of 18 and 35
What is the GCF of 18 and 35?
The GCF of 18 and 35 is 1. To calculate the greatest common factor of 18 and 35, we need to factor each number (factors of 18 = 1, 2, 3, 6, 9, 18; factors of 35 = 1, 5, 7, 35) and choose the greatest factor that exactly divides both 18 and 35, i.e., 1.
How to Find the GCF of 18 and 35 by Prime Factorization?
To find the GCF of 18 and 35, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 35 = 5 × 7.
⇒ There is no common prime factor for 18 and 35. Hence, GCF (18, 35) = 1.
☛ What is a Prime Number?
What is the Relation Between LCM and GCF of 18, 35?
The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 18 and 35, i.e. GCF × LCM = 18 × 35.
If the GCF of 35 and 18 is 1, Find its LCM.
GCF(35, 18) × LCM(35, 18) = 35 × 18
Since the GCF of 35 and 18 = 1
⇒ 1 × LCM(35, 18) = 630
Therefore, LCM = 630
☛ GCF Calculator
What are the Methods to Find GCF of 18 and 35?
There are three commonly used methods to find the GCF of 18 and 35.
- By Long Division
- By Euclidean Algorithm
- By Prime Factorization
How to Find the GCF of 18 and 35 by Long Division Method?
To find the GCF of 18, 35 using long division method, 35 is divided by 18. The corresponding divisor (1) when remainder equals 0 is taken as GCF.