Highest Common Factor of 204, 659, 78 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 204, 659, 78 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 204, 659, 78 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 204, 659, 78 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 204, 659, 78 is 1.
HCF(204, 659, 78) = 1
HCF of 204, 659, 78 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 204, 659, 78 is 1.
Highest Common Factor of 204,659,78 is 1
Step 1: Since 659 > 204, we apply the division lemma to 659 and 204, to get
659 = 204 x 3 + 47
Step 2: Since the reminder 204 ≠ 0, we apply division lemma to 47 and 204, to get
204 = 47 x 4 + 16
Step 3: We consider the new divisor 47 and the new remainder 16, and apply the division lemma to get
47 = 16 x 2 + 15
We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get
16 = 15 x 1 + 1
We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 204 and 659 is 1
Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(47,16) = HCF(204,47) = HCF(659,204) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 78 > 1, we apply the division lemma to 78 and 1, to get
78 = 1 x 78 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 78 is 1
Notice that 1 = HCF(78,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 204, 659, 78 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 204, 659, 78?
Answer: HCF of 204, 659, 78 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 204, 659, 78 using Euclid's Algorithm?
Answer: For arbitrary numbers 204, 659, 78 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.