Highest Common Factor of 567, 861, 978 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 567, 861, 978 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 567, 861, 978 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 567, 861, 978 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 567, 861, 978 is 3.
HCF(567, 861, 978) = 3
HCF of 567, 861, 978 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 567, 861, 978 is 3.
Highest Common Factor of 567,861,978 is 3
Step 1: Since 861 > 567, we apply the division lemma to 861 and 567, to get
861 = 567 x 1 + 294
Step 2: Since the reminder 567 ≠ 0, we apply division lemma to 294 and 567, to get
567 = 294 x 1 + 273
Step 3: We consider the new divisor 294 and the new remainder 273, and apply the division lemma to get
294 = 273 x 1 + 21
We consider the new divisor 273 and the new remainder 21, and apply the division lemma to get
273 = 21 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 567 and 861 is 21
Notice that 21 = HCF(273,21) = HCF(294,273) = HCF(567,294) = HCF(861,567) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 978 > 21, we apply the division lemma to 978 and 21, to get
978 = 21 x 46 + 12
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 12 and 21, to get
21 = 12 x 1 + 9
Step 3: We consider the new divisor 12 and the new remainder 9, and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3, and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 21 and 978 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(978,21) .
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Frequently Asked Questions on HCF of 567, 861, 978 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 567, 861, 978?
Answer: HCF of 567, 861, 978 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 567, 861, 978 using Euclid's Algorithm?
Answer: For arbitrary numbers 567, 861, 978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
