Highest Common Factor of 874, 9764 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 874, 9764 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 874, 9764 is 2 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 874, 9764 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 874, 9764 is 2.
HCF(874, 9764) = 2
HCF of 874, 9764 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 874, 9764 is 2.
Highest Common Factor of 874,9764 is 2
Step 1: Since 9764 > 874, we apply the division lemma to 9764 and 874, to get
9764 = 874 x 11 + 150
Step 2: Since the reminder 874 ≠ 0, we apply division lemma to 150 and 874, to get
874 = 150 x 5 + 124
Step 3: We consider the new divisor 150 and the new remainder 124, and apply the division lemma to get
150 = 124 x 1 + 26
We consider the new divisor 124 and the new remainder 26,and apply the division lemma to get
124 = 26 x 4 + 20
We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get
26 = 20 x 1 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 874 and 9764 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(124,26) = HCF(150,124) = HCF(874,150) = HCF(9764,874) .
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Frequently Asked Questions on HCF of 874, 9764 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 874, 9764?
Answer: HCF of 874, 9764 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 874, 9764 using Euclid's Algorithm?
Answer: For arbitrary numbers 874, 9764 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.