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 2607, 5786, 57711 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2607, 5786, 57711 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 2607, 5786, 57711 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 2607, 5786, 57711 is 1.
HCF(2607, 5786, 57711) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2607, 5786, 57711 is 1.
Step 1: Since 5786 > 2607, we apply the division lemma to 5786 and 2607, to get
5786 = 2607 x 2 + 572
Step 2: Since the reminder 2607 ≠ 0, we apply division lemma to 572 and 2607, to get
2607 = 572 x 4 + 319
Step 3: We consider the new divisor 572 and the new remainder 319, and apply the division lemma to get
572 = 319 x 1 + 253
We consider the new divisor 319 and the new remainder 253,and apply the division lemma to get
319 = 253 x 1 + 66
We consider the new divisor 253 and the new remainder 66,and apply the division lemma to get
253 = 66 x 3 + 55
We consider the new divisor 66 and the new remainder 55,and apply the division lemma to get
66 = 55 x 1 + 11
We consider the new divisor 55 and the new remainder 11,and apply the division lemma to get
55 = 11 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 2607 and 5786 is 11
Notice that 11 = HCF(55,11) = HCF(66,55) = HCF(253,66) = HCF(319,253) = HCF(572,319) = HCF(2607,572) = HCF(5786,2607) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 57711 > 11, we apply the division lemma to 57711 and 11, to get
57711 = 11 x 5246 + 5
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 5 and 11, to get
11 = 5 x 2 + 1
Step 3: 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 11 and 57711 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(57711,11) .
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 2607, 5786, 57711?
Answer: HCF of 2607, 5786, 57711 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2607, 5786, 57711 using Euclid's Algorithm?
Answer: For arbitrary numbers 2607, 5786, 57711 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.