HCF of 3, 4 and 5
HCF of 3, 4 and 5 is the largest possible number that divides 3, 4 and 5 exactly without any remainder. The factors of 3, 4 and 5 are (1, 3), (1, 2, 4) and (1, 5) respectively. There are 3 commonly used methods to find the HCF of 3, 4 and 5  prime factorization, Euclidean algorithm, and long division.
1.  HCF of 3, 4 and 5 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is HCF of 3, 4 and 5?
Answer: HCF of 3, 4 and 5 is 1.
Explanation:
The HCF of three nonzero integers, x(3), y(4) and z(5), is the highest positive integer m(1) that divides x(3), y(4) and z(5) without any remainder.
Methods to Find HCF of 3, 4 and 5
The methods to find the HCF of 3, 4 and 5 are explained below.
 Listing Common Factors
 Long Division Method
 Prime Factorization Method
HCF of 3, 4 and 5 by Listing Common Factors
 Factors of 3: 1, 3
 Factors of 4: 1, 2, 4
 Factors of 5: 1, 5
Since, 1 is the only common factor between 3, 4 and 5. The Highest Common Factor of 3, 4 and 5 is 1.
HCF of 3, 4 and 5 by Long Division
HCF of 3, 4 and 5 can be represented as HCF of (HCF of 3, 4) and 5. HCF(3, 4, 5) can be thus calculated by first finding HCF(3, 4) using long division and thereafter using this result with 5 to perform long division again.
 Step 1: Divide 4 (larger number) by 3 (smaller number).
 Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (3) by the remainder (1). Repeat this process until the remainder = 0.
⇒ HCF(3, 4) = 1.  Step 3: Now to find the HCF of 1 and 5, we will perform a long division on 5 and 1.
 Step 4: For remainder = 0, divisor = 1 ⇒ HCF(1, 5) = 1
Thus, HCF(3, 4, 5) = HCF(HCF(3, 4), 5) = 1.
HCF of 3, 4 and 5 by Prime Factorization
Prime factorization of 3, 4, and 5 is (3), (2 × 2), and (5) respectively. As visible, there are no common prime factors between 3, 4, and 5, i.e. they are coprime. Hence, the HCF of 3, 4, and 5 will be 1.
☛ Also Check:
 HCF of 4 and 6 = 2
 HCF of 3 and 6 = 3
 HCF of 255 and 867 = 51
 HCF of 294, 252 and 210 = 42
 HCF of 27 and 36 = 9
 HCF of 3 and 15 = 3
 HCF of 2 and 5 = 1
HCF of 3, 4 and 5 Examples

Example 1: Find the highest number that divides 3, 4, and 5 completely.
Solution:
The highest number that divides 3, 4, and 5 exactly is their highest common factor.
 Factors of 3 = 1, 3
 Factors of 4 = 1, 2, 4
 Factors of 5 = 1, 5
The HCF of 3, 4, and 5 is 1.
∴ The highest number that divides 3, 4, and 5 is 1. 
Example 2: Verify the relation between the LCM and HCF of 3, 4 and 5.
Solution:
The relation between the LCM and HCF of 3, 4 and 5 is given as, HCF(3, 4, 5) = [(3 × 4 × 5) × LCM(3, 4, 5)]/[LCM(3, 4) × LCM (4, 5) × LCM(3, 5)]
⇒ Prime factorization of 3, 4 and 5: 3 = 3
 4 = 2 × 2
 5 = 5
∴ LCM of (3, 4), (4, 5), (3, 5), and (3, 4, 5) is 12, 20, 15, and 60 respectively.
Now, LHS = HCF(3, 4, 5) = 1.
And, RHS = [(3 × 4 × 5) × LCM(3, 4, 5)]/[LCM(3, 4) × LCM (4, 5) × LCM(3, 5)] = [(60) × 60]/[12 × 20 × 15]
LHS = RHS = 1.
Hence verified. 
Example 3: Calculate the HCF of 3, 4, and 5 using LCM of the given numbers.
Solution:
Prime factorization of 3, 4 and 5 is given as,
 3 = 3
 4 = 2 × 2
 5 = 5
LCM(3, 4) = 12, LCM(4, 5) = 20, LCM(5, 3) = 15, LCM(3, 4, 5) = 60
⇒ HCF(3, 4, 5) = [(3 × 4 × 5) × LCM(3, 4, 5)]/[LCM(3, 4) × LCM (4, 5) × LCM(5, 3)]
⇒ HCF(3, 4, 5) = (60 × 60)/(12 × 20 × 15)
⇒ HCF(3, 4, 5) = 1.
Therefore, the HCF of 3, 4 and 5 is 1.
FAQs on HCF of 3, 4 and 5
What is the HCF of 3, 4 and 5?
The HCF of 3, 4 and 5 is 1. To calculate the HCF of 3, 4 and 5, we need to factor each number (factors of 3 = 1, 3; factors of 4 = 1, 2, 4; factors of 5 = 1, 5) and choose the highest factor that exactly divides 3, 4 and 5, i.e., 1.
Which of the following is HCF of 3, 4 and 5? 1, 48, 37, 27, 38, 41
HCF of 3, 4, 5 will be the number that divides 3, 4, and 5 without leaving any remainder. The only number that satisfies the given condition is 1.
How to Find the HCF of 3, 4 and 5 by Prime Factorization?
To find the HCF of 3, 4 and 5, we will find the prime factorization of given numbers, i.e. 3 = 3; 4 = 2 × 2; 5 = 5.
⇒ There is no common prime factor for 3, 4 and 5. Hence, HCF(3, 4, 5) = 1.
☛ What are Prime Numbers?
What is the Relation Between LCM and HCF of 3, 4 and 5?
The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 3, 4 and 5, i.e. HCF(3, 4, 5) = [(3 × 4 × 5) × LCM(3, 4, 5)]/[LCM(3, 4) × LCM (4, 5) × LCM(3, 5)].
☛ HCF Calculator
What are the Methods to Find HCF of 3, 4 and 5?
There are three commonly used methods to find the HCF of 3, 4 and 5.
 By Euclidean Algorithm
 By Prime Factorization
 By Long Division
visual curriculum