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 840, 582, 512, 35 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 840, 582, 512, 35 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 840, 582, 512, 35 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 840, 582, 512, 35 is 1.
HCF(840, 582, 512, 35) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 840, 582, 512, 35 is 1.
Step 1: Since 840 > 582, we apply the division lemma to 840 and 582, to get
840 = 582 x 1 + 258
Step 2: Since the reminder 582 ≠ 0, we apply division lemma to 258 and 582, to get
582 = 258 x 2 + 66
Step 3: We consider the new divisor 258 and the new remainder 66, and apply the division lemma to get
258 = 66 x 3 + 60
We consider the new divisor 66 and the new remainder 60,and apply the division lemma to get
66 = 60 x 1 + 6
We consider the new divisor 60 and the new remainder 6,and apply the division lemma to get
60 = 6 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 840 and 582 is 6
Notice that 6 = HCF(60,6) = HCF(66,60) = HCF(258,66) = HCF(582,258) = HCF(840,582) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 512 > 6, we apply the division lemma to 512 and 6, to get
512 = 6 x 85 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 512 is 2
Notice that 2 = HCF(6,2) = HCF(512,6) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 35 > 2, we apply the division lemma to 35 and 2, to get
35 = 2 x 17 + 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 35 is 1
Notice that 1 = HCF(2,1) = HCF(35,2) .
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 840, 582, 512, 35?
Answer: HCF of 840, 582, 512, 35 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 840, 582, 512, 35 using Euclid's Algorithm?
Answer: For arbitrary numbers 840, 582, 512, 35 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.