Highest Common Factor of 121, 684, 714 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 121, 684, 714 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 121, 684, 714 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 121, 684, 714 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 121, 684, 714 is 1.
HCF(121, 684, 714) = 1
HCF of 121, 684, 714 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 121, 684, 714 is 1.
Highest Common Factor of 121,684,714 is 1
Step 1: Since 684 > 121, we apply the division lemma to 684 and 121, to get
684 = 121 x 5 + 79
Step 2: Since the reminder 121 ≠ 0, we apply division lemma to 79 and 121, to get
121 = 79 x 1 + 42
Step 3: We consider the new divisor 79 and the new remainder 42, and apply the division lemma to get
79 = 42 x 1 + 37
We consider the new divisor 42 and the new remainder 37,and apply the division lemma to get
42 = 37 x 1 + 5
We consider the new divisor 37 and the new remainder 5,and apply the division lemma to get
37 = 5 x 7 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 121 and 684 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(37,5) = HCF(42,37) = HCF(79,42) = HCF(121,79) = HCF(684,121) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 714 > 1, we apply the division lemma to 714 and 1, to get
714 = 1 x 714 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 714 is 1
Notice that 1 = HCF(714,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 121, 684, 714 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 121, 684, 714?
Answer: HCF of 121, 684, 714 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 121, 684, 714 using Euclid's Algorithm?
Answer: For arbitrary numbers 121, 684, 714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
