Highest Common Factor of 684, 120, 478 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, 120, 478 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 120, 478 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, 120, 478 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, 120, 478 is 2.
HCF(684, 120, 478) = 2
HCF of 684, 120, 478 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, 120, 478 is 2.
Highest Common Factor of 684,120,478 is 2
Step 1: Since 684 > 120, we apply the division lemma to 684 and 120, to get
684 = 120 x 5 + 84
Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 84 and 120, to get
120 = 84 x 1 + 36
Step 3: We consider the new divisor 84 and the new remainder 36, and apply the division lemma to get
84 = 36 x 2 + 12
We consider the new divisor 36 and the new remainder 12, and apply the division lemma to get
36 = 12 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 684 and 120 is 12
Notice that 12 = HCF(36,12) = HCF(84,36) = HCF(120,84) = HCF(684,120) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 478 > 12, we apply the division lemma to 478 and 12, to get
478 = 12 x 39 + 10
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 10 and 12, to get
12 = 10 x 1 + 2
Step 3: We consider the new divisor 10 and the new remainder 2, and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 12 and 478 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(478,12) .
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Frequently Asked Questions on HCF of 684, 120, 478 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, 120, 478?
Answer: HCF of 684, 120, 478 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 120, 478 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 120, 478 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.