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 821, 592, 615 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 592, 615 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 821, 592, 615 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 821, 592, 615 is 1.
HCF(821, 592, 615) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 821, 592, 615 is 1.
Step 1: Since 821 > 592, we apply the division lemma to 821 and 592, to get
821 = 592 x 1 + 229
Step 2: Since the reminder 592 ≠ 0, we apply division lemma to 229 and 592, to get
592 = 229 x 2 + 134
Step 3: We consider the new divisor 229 and the new remainder 134, and apply the division lemma to get
229 = 134 x 1 + 95
We consider the new divisor 134 and the new remainder 95,and apply the division lemma to get
134 = 95 x 1 + 39
We consider the new divisor 95 and the new remainder 39,and apply the division lemma to get
95 = 39 x 2 + 17
We consider the new divisor 39 and the new remainder 17,and apply the division lemma to get
39 = 17 x 2 + 5
We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get
17 = 5 x 3 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 821 and 592 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(39,17) = HCF(95,39) = HCF(134,95) = HCF(229,134) = HCF(592,229) = HCF(821,592) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 615 > 1, we apply the division lemma to 615 and 1, to get
615 = 1 x 615 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 615 is 1
Notice that 1 = HCF(615,1) .
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 821, 592, 615?
Answer: HCF of 821, 592, 615 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 592, 615 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 592, 615 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.