Highest Common Factor of 547, 667 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 547, 667 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 547, 667 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 547, 667 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 547, 667 is 1.
HCF(547, 667) = 1
HCF of 547, 667 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 547, 667 is 1.
Highest Common Factor of 547,667 is 1
Step 1: Since 667 > 547, we apply the division lemma to 667 and 547, to get
667 = 547 x 1 + 120
Step 2: Since the reminder 547 ≠ 0, we apply division lemma to 120 and 547, to get
547 = 120 x 4 + 67
Step 3: We consider the new divisor 120 and the new remainder 67, and apply the division lemma to get
120 = 67 x 1 + 53
We consider the new divisor 67 and the new remainder 53,and apply the division lemma to get
67 = 53 x 1 + 14
We consider the new divisor 53 and the new remainder 14,and apply the division lemma to get
53 = 14 x 3 + 11
We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get
14 = 11 x 1 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 547 and 667 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(53,14) = HCF(67,53) = HCF(120,67) = HCF(547,120) = HCF(667,547) .
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Frequently Asked Questions on HCF of 547, 667 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 547, 667?
Answer: HCF of 547, 667 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 547, 667 using Euclid's Algorithm?
Answer: For arbitrary numbers 547, 667 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
