GCF of 3 and 5
GCF of 3 and 5 is the largest possible number that divides 3 and 5 exactly without any remainder. The factors of 3 and 5 are 1, 3 and 1, 5 respectively. There are 3 commonly used methods to find the GCF of 3 and 5 - prime factorization, long division, and Euclidean algorithm.
1. | GCF of 3 and 5 |
2. | List of Methods |
3. | Solved Examples |
4. | FAQs |
What is GCF of 3 and 5?
Answer: GCF of 3 and 5 is 1.
Explanation:
The GCF of two non-zero integers, x(3) and y(5), is the greatest positive integer m(1) that divides both x(3) and y(5) without any remainder.
Methods to Find GCF of 3 and 5
The methods to find the GCF of 3 and 5 are explained below.
- Listing Common Factors
- Prime Factorization Method
- Long Division Method
GCF of 3 and 5 by Listing Common Factors
- Factors of 3: 1, 3
- Factors of 5: 1, 5
Since, 1 is the only common factor between 3 and 5. The Greatest Common Factor of 3 and 5 is 1.
GCF of 3 and 5 by Prime Factorization
Prime factorization of 3 and 5 is (3) and (5) respectively. As visible, there are no common prime factors between 3 and 5, i.e. they are co-prime. Hence, the GCF of 3 and 5 will be 1.
GCF of 3 and 5 by Long Division
GCF of 3 and 5 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.
- Step 1: Divide 5 (larger number) by 3 (smaller number).
- Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (3) by the remainder (2).
- Step 3: Repeat this process until the remainder = 0.
The corresponding divisor (1) is the GCF of 3 and 5.
☛ Also Check:
- GCF of 72 and 84 = 12
- GCF of 21 and 24 = 3
- GCF of 32 and 81 = 1
- GCF of 56 and 64 = 8
- GCF of 2 and 8 = 2
- GCF of 35 and 63 = 7
- GCF of 22 and 44 = 22
GCF of 3 and 5 Examples
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Example 1: The product of two numbers is 15. If their GCF is 1, what is their LCM?
Solution:
Given: GCF = 1 and product of numbers = 15
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 15/1
Therefore, the LCM is 15. -
Example 2: Find the greatest number that divides 3 and 5 exactly.
Solution:
The greatest number that divides 3 and 5 exactly is their greatest common factor, i.e. GCF of 3 and 5.
⇒ Factors of 3 and 5:- Factors of 3 = 1, 3
- Factors of 5 = 1, 5
Therefore, the GCF of 3 and 5 is 1.
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Example 3: Find the GCF of 3 and 5, if their LCM is 15.
Solution:
∵ LCM × GCF = 3 × 5
⇒ GCF(3, 5) = (3 × 5)/15 = 1
Therefore, the greatest common factor of 3 and 5 is 1.
FAQs on GCF of 3 and 5
What is the GCF of 3 and 5?
The GCF of 3 and 5 is 1. To calculate the greatest common factor (GCF) of 3 and 5, we need to factor each number (factors of 3 = 1, 3; factors of 5 = 1, 5) and choose the greatest factor that exactly divides both 3 and 5, i.e., 1.
What are the Methods to Find GCF of 3 and 5?
There are three commonly used methods to find the GCF of 3 and 5.
- By Prime Factorization
- By Long Division
- By Listing Common Factors
What is the Relation Between LCM and GCF of 3, 5?
The following equation can be used to express the relation between LCM and GCF of 3 and 5, i.e. GCF × LCM = 3 × 5.
How to Find the GCF of 3 and 5 by Long Division Method?
To find the GCF of 3, 5 using long division method, 5 is divided by 3. The corresponding divisor (1) when remainder equals 0 is taken as GCF.
If the GCF of 5 and 3 is 1, Find its LCM.
GCF(5, 3) × LCM(5, 3) = 5 × 3
Since the GCF of 5 and 3 = 1
⇒ 1 × LCM(5, 3) = 15
Therefore, LCM = 15
☛ GCF Calculator
How to Find the GCF of 3 and 5 by Prime Factorization?
To find the GCF of 3 and 5, we will find the prime factorization of the given numbers, i.e. 3 = 3; 5 = 5.
⇒ There is no common prime factor for 3 and 5. Hence, GCF (3, 5) = 1.
☛ What are Prime Numbers?
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