Highest Common Factor of 564, 645, 109, 214 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, 645, 109, 214 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 564, 645, 109, 214 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, 645, 109, 214 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, 645, 109, 214 is 1.
HCF(564, 645, 109, 214) = 1
HCF of 564, 645, 109, 214 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, 645, 109, 214 is 1.
Highest Common Factor of 564,645,109,214 is 1
Step 1: Since 645 > 564, we apply the division lemma to 645 and 564, to get
645 = 564 x 1 + 81
Step 2: Since the reminder 564 ≠ 0, we apply division lemma to 81 and 564, to get
564 = 81 x 6 + 78
Step 3: We consider the new divisor 81 and the new remainder 78, and apply the division lemma to get
81 = 78 x 1 + 3
We consider the new divisor 78 and the new remainder 3, and apply the division lemma to get
78 = 3 x 26 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 564 and 645 is 3
Notice that 3 = HCF(78,3) = HCF(81,78) = HCF(564,81) = HCF(645,564) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 109 > 3, we apply the division lemma to 109 and 3, to get
109 = 3 x 36 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 109 is 1
Notice that 1 = HCF(3,1) = HCF(109,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 214 > 1, we apply the division lemma to 214 and 1, to get
214 = 1 x 214 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 214 is 1
Notice that 1 = HCF(214,1) .
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Frequently Asked Questions on HCF of 564, 645, 109, 214 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, 645, 109, 214?
Answer: HCF of 564, 645, 109, 214 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 564, 645, 109, 214 using Euclid's Algorithm?
Answer: For arbitrary numbers 564, 645, 109, 214 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.