Highest Common Factor of 667, 474 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 667, 474 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 667, 474 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 667, 474 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 667, 474 is 1.
HCF(667, 474) = 1
HCF of 667, 474 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 667, 474 is 1.
Highest Common Factor of 667,474 is 1
Step 1: Since 667 > 474, we apply the division lemma to 667 and 474, to get
667 = 474 x 1 + 193
Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 193 and 474, to get
474 = 193 x 2 + 88
Step 3: We consider the new divisor 193 and the new remainder 88, and apply the division lemma to get
193 = 88 x 2 + 17
We consider the new divisor 88 and the new remainder 17,and apply the division lemma to get
88 = 17 x 5 + 3
We consider the new divisor 17 and the new remainder 3,and apply the division lemma to get
17 = 3 x 5 + 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 667 and 474 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(17,3) = HCF(88,17) = HCF(193,88) = HCF(474,193) = HCF(667,474) .
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Frequently Asked Questions on HCF of 667, 474 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 667, 474?
Answer: HCF of 667, 474 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 667, 474 using Euclid's Algorithm?
Answer: For arbitrary numbers 667, 474 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.