Highest Common Factor of 423, 689, 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 423, 689, 714 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 423, 689, 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 423, 689, 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 423, 689, 714 is 1.
HCF(423, 689, 714) = 1
HCF of 423, 689, 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 423, 689, 714 is 1.
Highest Common Factor of 423,689,714 is 1
Step 1: Since 689 > 423, we apply the division lemma to 689 and 423, to get
689 = 423 x 1 + 266
Step 2: Since the reminder 423 ≠ 0, we apply division lemma to 266 and 423, to get
423 = 266 x 1 + 157
Step 3: We consider the new divisor 266 and the new remainder 157, and apply the division lemma to get
266 = 157 x 1 + 109
We consider the new divisor 157 and the new remainder 109,and apply the division lemma to get
157 = 109 x 1 + 48
We consider the new divisor 109 and the new remainder 48,and apply the division lemma to get
109 = 48 x 2 + 13
We consider the new divisor 48 and the new remainder 13,and apply the division lemma to get
48 = 13 x 3 + 9
We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get
13 = 9 x 1 + 4
We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get
9 = 4 x 2 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 423 and 689 is 1
Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(48,13) = HCF(109,48) = HCF(157,109) = HCF(266,157) = HCF(423,266) = HCF(689,423) .
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 423, 689, 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 423, 689, 714?
Answer: HCF of 423, 689, 714 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 423, 689, 714 using Euclid's Algorithm?
Answer: For arbitrary numbers 423, 689, 714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
