Highest Common Factor of 60, 594, 867 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 60, 594, 867 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 60, 594, 867 is 3 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 60, 594, 867 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 60, 594, 867 is 3.
HCF(60, 594, 867) = 3
HCF of 60, 594, 867 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 60, 594, 867 is 3.
Highest Common Factor of 60,594,867 is 3
Step 1: Since 594 > 60, we apply the division lemma to 594 and 60, to get
594 = 60 x 9 + 54
Step 2: Since the reminder 60 ≠ 0, we apply division lemma to 54 and 60, to get
60 = 54 x 1 + 6
Step 3: We consider the new divisor 54 and the new remainder 6, and apply the division lemma to get
54 = 6 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 60 and 594 is 6
Notice that 6 = HCF(54,6) = HCF(60,54) = HCF(594,60) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 867 > 6, we apply the division lemma to 867 and 6, to get
867 = 6 x 144 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 867 is 3
Notice that 3 = HCF(6,3) = HCF(867,6) .
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Frequently Asked Questions on HCF of 60, 594, 867 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 60, 594, 867?
Answer: HCF of 60, 594, 867 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 60, 594, 867 using Euclid's Algorithm?
Answer: For arbitrary numbers 60, 594, 867 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.