Highest Common Factor of 872, 204, 60, 664 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 872, 204, 60, 664 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 872, 204, 60, 664 is 4 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 872, 204, 60, 664 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 872, 204, 60, 664 is 4.
HCF(872, 204, 60, 664) = 4
HCF of 872, 204, 60, 664 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 872, 204, 60, 664 is 4.
Highest Common Factor of 872,204,60,664 is 4
Step 1: Since 872 > 204, we apply the division lemma to 872 and 204, to get
872 = 204 x 4 + 56
Step 2: Since the reminder 204 ≠ 0, we apply division lemma to 56 and 204, to get
204 = 56 x 3 + 36
Step 3: We consider the new divisor 56 and the new remainder 36, and apply the division lemma to get
56 = 36 x 1 + 20
We consider the new divisor 36 and the new remainder 20,and apply the division lemma to get
36 = 20 x 1 + 16
We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get
20 = 16 x 1 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 872 and 204 is 4
Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(36,20) = HCF(56,36) = HCF(204,56) = HCF(872,204) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 60 > 4, we apply the division lemma to 60 and 4, to get
60 = 4 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 60 is 4
Notice that 4 = HCF(60,4) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 664 > 4, we apply the division lemma to 664 and 4, to get
664 = 4 x 166 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 664 is 4
Notice that 4 = HCF(664,4) .
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Frequently Asked Questions on HCF of 872, 204, 60, 664 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 872, 204, 60, 664?
Answer: HCF of 872, 204, 60, 664 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 872, 204, 60, 664 using Euclid's Algorithm?
Answer: For arbitrary numbers 872, 204, 60, 664 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
