Highest Common Factor of 453, 684 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 453, 684 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 453, 684 is 3 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 453, 684 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 453, 684 is 3.
HCF(453, 684) = 3
HCF of 453, 684 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 453, 684 is 3.
Highest Common Factor of 453,684 is 3
Step 1: Since 684 > 453, we apply the division lemma to 684 and 453, to get
684 = 453 x 1 + 231
Step 2: Since the reminder 453 ≠ 0, we apply division lemma to 231 and 453, to get
453 = 231 x 1 + 222
Step 3: We consider the new divisor 231 and the new remainder 222, and apply the division lemma to get
231 = 222 x 1 + 9
We consider the new divisor 222 and the new remainder 9,and apply the division lemma to get
222 = 9 x 24 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 453 and 684 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(222,9) = HCF(231,222) = HCF(453,231) = HCF(684,453) .
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Frequently Asked Questions on HCF of 453, 684 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 453, 684?
Answer: HCF of 453, 684 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 453, 684 using Euclid's Algorithm?
Answer: For arbitrary numbers 453, 684 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.