Highest Common Factor of 837, 558, 648 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 837, 558, 648 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 837, 558, 648 is 9 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 837, 558, 648 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 837, 558, 648 is 9.
HCF(837, 558, 648) = 9
HCF of 837, 558, 648 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 837, 558, 648 is 9.
Highest Common Factor of 837,558,648 is 9
Step 1: Since 837 > 558, we apply the division lemma to 837 and 558, to get
837 = 558 x 1 + 279
Step 2: Since the reminder 558 ≠ 0, we apply division lemma to 279 and 558, to get
558 = 279 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 279, the HCF of 837 and 558 is 279
Notice that 279 = HCF(558,279) = HCF(837,558) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 648 > 279, we apply the division lemma to 648 and 279, to get
648 = 279 x 2 + 90
Step 2: Since the reminder 279 ≠ 0, we apply division lemma to 90 and 279, to get
279 = 90 x 3 + 9
Step 3: We consider the new divisor 90 and the new remainder 9, and apply the division lemma to get
90 = 9 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 279 and 648 is 9
Notice that 9 = HCF(90,9) = HCF(279,90) = HCF(648,279) .
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Frequently Asked Questions on HCF of 837, 558, 648 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 837, 558, 648?
Answer: HCF of 837, 558, 648 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 837, 558, 648 using Euclid's Algorithm?
Answer: For arbitrary numbers 837, 558, 648 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.