Highest Common Factor of 873, 679, 192, 66 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 873, 679, 192, 66 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 873, 679, 192, 66 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 873, 679, 192, 66 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 873, 679, 192, 66 is 1.
HCF(873, 679, 192, 66) = 1
HCF of 873, 679, 192, 66 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 873, 679, 192, 66 is 1.
Highest Common Factor of 873,679,192,66 is 1
Step 1: Since 873 > 679, we apply the division lemma to 873 and 679, to get
873 = 679 x 1 + 194
Step 2: Since the reminder 679 ≠ 0, we apply division lemma to 194 and 679, to get
679 = 194 x 3 + 97
Step 3: We consider the new divisor 194 and the new remainder 97, and apply the division lemma to get
194 = 97 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 97, the HCF of 873 and 679 is 97
Notice that 97 = HCF(194,97) = HCF(679,194) = HCF(873,679) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 192 > 97, we apply the division lemma to 192 and 97, to get
192 = 97 x 1 + 95
Step 2: Since the reminder 97 ≠ 0, we apply division lemma to 95 and 97, to get
97 = 95 x 1 + 2
Step 3: We consider the new divisor 95 and the new remainder 2, and apply the division lemma to get
95 = 2 x 47 + 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 97 and 192 is 1
Notice that 1 = HCF(2,1) = HCF(95,2) = HCF(97,95) = HCF(192,97) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 66 > 1, we apply the division lemma to 66 and 1, to get
66 = 1 x 66 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 66 is 1
Notice that 1 = HCF(66,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 873, 679, 192, 66 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 873, 679, 192, 66?
Answer: HCF of 873, 679, 192, 66 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 873, 679, 192, 66 using Euclid's Algorithm?
Answer: For arbitrary numbers 873, 679, 192, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.