Highest Common Factor of 414, 667, 729, 568 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 414, 667, 729, 568 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 414, 667, 729, 568 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 414, 667, 729, 568 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 414, 667, 729, 568 is 1.
HCF(414, 667, 729, 568) = 1
HCF of 414, 667, 729, 568 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 414, 667, 729, 568 is 1.
Highest Common Factor of 414,667,729,568 is 1
Step 1: Since 667 > 414, we apply the division lemma to 667 and 414, to get
667 = 414 x 1 + 253
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 253 and 414, to get
414 = 253 x 1 + 161
Step 3: We consider the new divisor 253 and the new remainder 161, and apply the division lemma to get
253 = 161 x 1 + 92
We consider the new divisor 161 and the new remainder 92,and apply the division lemma to get
161 = 92 x 1 + 69
We consider the new divisor 92 and the new remainder 69,and apply the division lemma to get
92 = 69 x 1 + 23
We consider the new divisor 69 and the new remainder 23,and apply the division lemma to get
69 = 23 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 23, the HCF of 414 and 667 is 23
Notice that 23 = HCF(69,23) = HCF(92,69) = HCF(161,92) = HCF(253,161) = HCF(414,253) = HCF(667,414) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 729 > 23, we apply the division lemma to 729 and 23, to get
729 = 23 x 31 + 16
Step 2: Since the reminder 23 ≠ 0, we apply division lemma to 16 and 23, to get
23 = 16 x 1 + 7
Step 3: We consider the new divisor 16 and the new remainder 7, and apply the division lemma to get
16 = 7 x 2 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 23 and 729 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(23,16) = HCF(729,23) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 568 > 1, we apply the division lemma to 568 and 1, to get
568 = 1 x 568 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 568 is 1
Notice that 1 = HCF(568,1) .
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Frequently Asked Questions on HCF of 414, 667, 729, 568 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 414, 667, 729, 568?
Answer: HCF of 414, 667, 729, 568 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 414, 667, 729, 568 using Euclid's Algorithm?
Answer: For arbitrary numbers 414, 667, 729, 568 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.