Highest Common Factor of 335, 308, 42, 109 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 335, 308, 42, 109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 335, 308, 42, 109 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 335, 308, 42, 109 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 335, 308, 42, 109 is 1.
HCF(335, 308, 42, 109) = 1
HCF of 335, 308, 42, 109 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 335, 308, 42, 109 is 1.
Highest Common Factor of 335,308,42,109 is 1
Step 1: Since 335 > 308, we apply the division lemma to 335 and 308, to get
335 = 308 x 1 + 27
Step 2: Since the reminder 308 ≠ 0, we apply division lemma to 27 and 308, to get
308 = 27 x 11 + 11
Step 3: We consider the new divisor 27 and the new remainder 11, and apply the division lemma to get
27 = 11 x 2 + 5
We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get
11 = 5 x 2 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 335 and 308 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(27,11) = HCF(308,27) = HCF(335,308) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 1, we apply the division lemma to 42 and 1, to get
42 = 1 x 42 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 42 is 1
Notice that 1 = HCF(42,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 109 > 1, we apply the division lemma to 109 and 1, to get
109 = 1 x 109 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 109 is 1
Notice that 1 = HCF(109,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 335, 308, 42, 109 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 335, 308, 42, 109?
Answer: HCF of 335, 308, 42, 109 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 335, 308, 42, 109 using Euclid's Algorithm?
Answer: For arbitrary numbers 335, 308, 42, 109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.