Highest Common Factor of 684, 454 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, 454 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 454 is 2 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, 454 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, 454 is 2.
HCF(684, 454) = 2
HCF of 684, 454 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, 454 is 2.
Highest Common Factor of 684,454 is 2
Step 1: Since 684 > 454, we apply the division lemma to 684 and 454, to get
684 = 454 x 1 + 230
Step 2: Since the reminder 454 ≠ 0, we apply division lemma to 230 and 454, to get
454 = 230 x 1 + 224
Step 3: We consider the new divisor 230 and the new remainder 224, and apply the division lemma to get
230 = 224 x 1 + 6
We consider the new divisor 224 and the new remainder 6,and apply the division lemma to get
224 = 6 x 37 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 684 and 454 is 2
Notice that 2 = HCF(6,2) = HCF(224,6) = HCF(230,224) = HCF(454,230) = HCF(684,454) .
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, 454 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, 454?
Answer: HCF of 684, 454 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 454 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 454 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.