Highest Common Factor of 684, 906, 47 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, 906, 47 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 684, 906, 47 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 684, 906, 47 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, 906, 47 is 1.
HCF(684, 906, 47) = 1
HCF of 684, 906, 47 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, 906, 47 is 1.
Highest Common Factor of 684,906,47 is 1
Step 1: Since 906 > 684, we apply the division lemma to 906 and 684, to get
906 = 684 x 1 + 222
Step 2: Since the reminder 684 ≠ 0, we apply division lemma to 222 and 684, to get
684 = 222 x 3 + 18
Step 3: We consider the new divisor 222 and the new remainder 18, and apply the division lemma to get
222 = 18 x 12 + 6
We consider the new divisor 18 and the new remainder 6, and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 684 and 906 is 6
Notice that 6 = HCF(18,6) = HCF(222,18) = HCF(684,222) = HCF(906,684) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 47 > 6, we apply the division lemma to 47 and 6, to get
47 = 6 x 7 + 5
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get
6 = 5 x 1 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 47 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(47,6) .
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Frequently Asked Questions on HCF of 684, 906, 47 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, 906, 47?
Answer: HCF of 684, 906, 47 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 684, 906, 47 using Euclid's Algorithm?
Answer: For arbitrary numbers 684, 906, 47 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.