Highest Common Factor of 921, 6828 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 921, 6828 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 921, 6828 is 3 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 921, 6828 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 921, 6828 is 3.
HCF(921, 6828) = 3
HCF of 921, 6828 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 921, 6828 is 3.
Highest Common Factor of 921,6828 is 3
Step 1: Since 6828 > 921, we apply the division lemma to 6828 and 921, to get
6828 = 921 x 7 + 381
Step 2: Since the reminder 921 ≠ 0, we apply division lemma to 381 and 921, to get
921 = 381 x 2 + 159
Step 3: We consider the new divisor 381 and the new remainder 159, and apply the division lemma to get
381 = 159 x 2 + 63
We consider the new divisor 159 and the new remainder 63,and apply the division lemma to get
159 = 63 x 2 + 33
We consider the new divisor 63 and the new remainder 33,and apply the division lemma to get
63 = 33 x 1 + 30
We consider the new divisor 33 and the new remainder 30,and apply the division lemma to get
33 = 30 x 1 + 3
We consider the new divisor 30 and the new remainder 3,and apply the division lemma to get
30 = 3 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 921 and 6828 is 3
Notice that 3 = HCF(30,3) = HCF(33,30) = HCF(63,33) = HCF(159,63) = HCF(381,159) = HCF(921,381) = HCF(6828,921) .
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Frequently Asked Questions on HCF of 921, 6828 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 921, 6828?
Answer: HCF of 921, 6828 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 921, 6828 using Euclid's Algorithm?
Answer: For arbitrary numbers 921, 6828 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.