Highest Common Factor of 803, 51221 using Euclid's algorithm
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 803, 51221 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 803, 51221 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 803, 51221 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 803, 51221 is 1.
HCF(803, 51221) = 1
HCF of 803, 51221 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 803, 51221 is 1.
Highest Common Factor of 803,51221 is 1
Step 1: Since 51221 > 803, we apply the division lemma to 51221 and 803, to get
51221 = 803 x 63 + 632
Step 2: Since the reminder 803 ≠ 0, we apply division lemma to 632 and 803, to get
803 = 632 x 1 + 171
Step 3: We consider the new divisor 632 and the new remainder 171, and apply the division lemma to get
632 = 171 x 3 + 119
We consider the new divisor 171 and the new remainder 119,and apply the division lemma to get
171 = 119 x 1 + 52
We consider the new divisor 119 and the new remainder 52,and apply the division lemma to get
119 = 52 x 2 + 15
We consider the new divisor 52 and the new remainder 15,and apply the division lemma to get
52 = 15 x 3 + 7
We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get
15 = 7 x 2 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 803 and 51221 is 1
Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(52,15) = HCF(119,52) = HCF(171,119) = HCF(632,171) = HCF(803,632) = HCF(51221,803) .
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Frequently Asked Questions on HCF of 803, 51221 using Euclid's Algorithm
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 803, 51221?
Answer: HCF of 803, 51221 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 803, 51221 using Euclid's Algorithm?
Answer: For arbitrary numbers 803, 51221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.