Highest Common Factor of 858, 705, 912 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 858, 705, 912 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 858, 705, 912 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 858, 705, 912 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 858, 705, 912 is 3.
HCF(858, 705, 912) = 3
HCF of 858, 705, 912 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 858, 705, 912 is 3.
Highest Common Factor of 858,705,912 is 3
Step 1: Since 858 > 705, we apply the division lemma to 858 and 705, to get
858 = 705 x 1 + 153
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 153 and 705, to get
705 = 153 x 4 + 93
Step 3: We consider the new divisor 153 and the new remainder 93, and apply the division lemma to get
153 = 93 x 1 + 60
We consider the new divisor 93 and the new remainder 60,and apply the division lemma to get
93 = 60 x 1 + 33
We consider the new divisor 60 and the new remainder 33,and apply the division lemma to get
60 = 33 x 1 + 27
We consider the new divisor 33 and the new remainder 27,and apply the division lemma to get
33 = 27 x 1 + 6
We consider the new divisor 27 and the new remainder 6,and apply the division lemma to get
27 = 6 x 4 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma 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 858 and 705 is 3
Notice that 3 = HCF(6,3) = HCF(27,6) = HCF(33,27) = HCF(60,33) = HCF(93,60) = HCF(153,93) = HCF(705,153) = HCF(858,705) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 912 > 3, we apply the division lemma to 912 and 3, to get
912 = 3 x 304 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 912 is 3
Notice that 3 = HCF(912,3) .
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Frequently Asked Questions on HCF of 858, 705, 912 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 858, 705, 912?
Answer: HCF of 858, 705, 912 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 858, 705, 912 using Euclid's Algorithm?
Answer: For arbitrary numbers 858, 705, 912 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.