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, 66315 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 821, 66315 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, 66315 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, 66315 is 1.
HCF(821, 66315) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 821, 66315 is 1.
Step 1: Since 66315 > 821, we apply the division lemma to 66315 and 821, to get
66315 = 821 x 80 + 635
Step 2: Since the reminder 821 ≠ 0, we apply division lemma to 635 and 821, to get
821 = 635 x 1 + 186
Step 3: We consider the new divisor 635 and the new remainder 186, and apply the division lemma to get
635 = 186 x 3 + 77
We consider the new divisor 186 and the new remainder 77,and apply the division lemma to get
186 = 77 x 2 + 32
We consider the new divisor 77 and the new remainder 32,and apply the division lemma to get
77 = 32 x 2 + 13
We consider the new divisor 32 and the new remainder 13,and apply the division lemma to get
32 = 13 x 2 + 6
We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get
13 = 6 x 2 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 66315 is 1
Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(32,13) = HCF(77,32) = HCF(186,77) = HCF(635,186) = HCF(821,635) = HCF(66315,821) .
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, 66315?
Answer: HCF of 821, 66315 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 821, 66315 using Euclid's Algorithm?
Answer: For arbitrary numbers 821, 66315 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.