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, 538, 691 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 858, 538, 691 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 858, 538, 691 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, 538, 691 is 1.
HCF(858, 538, 691) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 858, 538, 691 is 1.
Step 1: Since 858 > 538, we apply the division lemma to 858 and 538, to get
858 = 538 x 1 + 320
Step 2: Since the reminder 538 ≠ 0, we apply division lemma to 320 and 538, to get
538 = 320 x 1 + 218
Step 3: We consider the new divisor 320 and the new remainder 218, and apply the division lemma to get
320 = 218 x 1 + 102
We consider the new divisor 218 and the new remainder 102,and apply the division lemma to get
218 = 102 x 2 + 14
We consider the new divisor 102 and the new remainder 14,and apply the division lemma to get
102 = 14 x 7 + 4
We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get
14 = 4 x 3 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 858 and 538 is 2
Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(102,14) = HCF(218,102) = HCF(320,218) = HCF(538,320) = HCF(858,538) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 691 > 2, we apply the division lemma to 691 and 2, to get
691 = 2 x 345 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 691 is 1
Notice that 1 = HCF(2,1) = HCF(691,2) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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, 538, 691?
Answer: HCF of 858, 538, 691 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 858, 538, 691 using Euclid's Algorithm?
Answer: For arbitrary numbers 858, 538, 691 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.