Highest Common Factor of 684, 103, 155, 762 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 684, 103, 155, 762 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 103, 155, 762 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 684, 103, 155, 762 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 684, 103, 155, 762 is 1.
HCF(684, 103, 155, 762) = 1
HCF of 684, 103, 155, 762 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 684, 103, 155, 762 is 1.
Highest Common Factor of 684,103,155,762 is 1
Step 1: Since 684 > 103, we apply the division lemma to 684 and 103, to get
684 = 103 x 6 + 66
Step 2: Since the reminder 103 ≠ 0, we apply division lemma to 66 and 103, to get
103 = 66 x 1 + 37
Step 3: We consider the new divisor 66 and the new remainder 37, and apply the division lemma to get
66 = 37 x 1 + 29
We consider the new divisor 37 and the new remainder 29,and apply the division lemma to get
37 = 29 x 1 + 8
We consider the new divisor 29 and the new remainder 8,and apply the division lemma to get
29 = 8 x 3 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 684 and 103 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(29,8) = HCF(37,29) = HCF(66,37) = HCF(103,66) = HCF(684,103) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 155 > 1, we apply the division lemma to 155 and 1, to get
155 = 1 x 155 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 155 is 1
Notice that 1 = HCF(155,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 762 > 1, we apply the division lemma to 762 and 1, to get
762 = 1 x 762 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 762 is 1
Notice that 1 = HCF(762,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 684, 103, 155, 762 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 684, 103, 155, 762?
Answer: HCF of 684, 103, 155, 762 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 103, 155, 762 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 103, 155, 762 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.