Highest Common Factor of 855, 585, 107 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 855, 585, 107 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 855, 585, 107 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 855, 585, 107 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 855, 585, 107 is 1.
HCF(855, 585, 107) = 1
HCF of 855, 585, 107 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 855, 585, 107 is 1.
Highest Common Factor of 855,585,107 is 1
Step 1: Since 855 > 585, we apply the division lemma to 855 and 585, to get
855 = 585 x 1 + 270
Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 270 and 585, to get
585 = 270 x 2 + 45
Step 3: We consider the new divisor 270 and the new remainder 45, and apply the division lemma to get
270 = 45 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 855 and 585 is 45
Notice that 45 = HCF(270,45) = HCF(585,270) = HCF(855,585) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 107 > 45, we apply the division lemma to 107 and 45, to get
107 = 45 x 2 + 17
Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 17 and 45, to get
45 = 17 x 2 + 11
Step 3: We consider the new divisor 17 and the new remainder 11, and apply the division lemma to get
17 = 11 x 1 + 6
We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 45 and 107 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(45,17) = HCF(107,45) .
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Frequently Asked Questions on HCF of 855, 585, 107 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 855, 585, 107?
Answer: HCF of 855, 585, 107 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 855, 585, 107 using Euclid's Algorithm?
Answer: For arbitrary numbers 855, 585, 107 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
