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, 538, 709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 840, 538, 709 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, 538, 709 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, 538, 709 is 1.
HCF(840, 538, 709) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 840, 538, 709 is 1.
Step 1: Since 840 > 538, we apply the division lemma to 840 and 538, to get
840 = 538 x 1 + 302
Step 2: Since the reminder 538 ≠ 0, we apply division lemma to 302 and 538, to get
538 = 302 x 1 + 236
Step 3: We consider the new divisor 302 and the new remainder 236, and apply the division lemma to get
302 = 236 x 1 + 66
We consider the new divisor 236 and the new remainder 66,and apply the division lemma to get
236 = 66 x 3 + 38
We consider the new divisor 66 and the new remainder 38,and apply the division lemma to get
66 = 38 x 1 + 28
We consider the new divisor 38 and the new remainder 28,and apply the division lemma to get
38 = 28 x 1 + 10
We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get
28 = 10 x 2 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 840 and 538 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(38,28) = HCF(66,38) = HCF(236,66) = HCF(302,236) = HCF(538,302) = HCF(840,538) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 709 > 2, we apply the division lemma to 709 and 2, to get
709 = 2 x 354 + 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 709 is 1
Notice that 1 = HCF(2,1) = HCF(709,2) .
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, 538, 709?
Answer: HCF of 840, 538, 709 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 840, 538, 709 using Euclid's Algorithm?
Answer: For arbitrary numbers 840, 538, 709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.