Highest Common Factor of 564, 912, 514, 91 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 564, 912, 514, 91 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 564, 912, 514, 91 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 564, 912, 514, 91 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 564, 912, 514, 91 is 1.
HCF(564, 912, 514, 91) = 1
HCF of 564, 912, 514, 91 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 564, 912, 514, 91 is 1.
Highest Common Factor of 564,912,514,91 is 1
Step 1: Since 912 > 564, we apply the division lemma to 912 and 564, to get
912 = 564 x 1 + 348
Step 2: Since the reminder 564 ≠ 0, we apply division lemma to 348 and 564, to get
564 = 348 x 1 + 216
Step 3: We consider the new divisor 348 and the new remainder 216, and apply the division lemma to get
348 = 216 x 1 + 132
We consider the new divisor 216 and the new remainder 132,and apply the division lemma to get
216 = 132 x 1 + 84
We consider the new divisor 132 and the new remainder 84,and apply the division lemma to get
132 = 84 x 1 + 48
We consider the new divisor 84 and the new remainder 48,and apply the division lemma to get
84 = 48 x 1 + 36
We consider the new divisor 48 and the new remainder 36,and apply the division lemma to get
48 = 36 x 1 + 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 564 and 912 is 12
Notice that 12 = HCF(36,12) = HCF(48,36) = HCF(84,48) = HCF(132,84) = HCF(216,132) = HCF(348,216) = HCF(564,348) = HCF(912,564) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 514 > 12, we apply the division lemma to 514 and 12, to get
514 = 12 x 42 + 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 514 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(514,12) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 91 > 2, we apply the division lemma to 91 and 2, to get
91 = 2 x 45 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 91 is 1
Notice that 1 = HCF(2,1) = HCF(91,2) .
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Frequently Asked Questions on HCF of 564, 912, 514, 91 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 564, 912, 514, 91?
Answer: HCF of 564, 912, 514, 91 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 564, 912, 514, 91 using Euclid's Algorithm?
Answer: For arbitrary numbers 564, 912, 514, 91 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.