Highest Common Factor of 8922, 1178 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 8922, 1178 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 8922, 1178 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 8922, 1178 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 8922, 1178 is 2.
HCF(8922, 1178) = 2
HCF of 8922, 1178 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8922, 1178 is 2.
Highest Common Factor of 8922,1178 is 2
Step 1: Since 8922 > 1178, we apply the division lemma to 8922 and 1178, to get
8922 = 1178 x 7 + 676
Step 2: Since the reminder 1178 ≠ 0, we apply division lemma to 676 and 1178, to get
1178 = 676 x 1 + 502
Step 3: We consider the new divisor 676 and the new remainder 502, and apply the division lemma to get
676 = 502 x 1 + 174
We consider the new divisor 502 and the new remainder 174,and apply the division lemma to get
502 = 174 x 2 + 154
We consider the new divisor 174 and the new remainder 154,and apply the division lemma to get
174 = 154 x 1 + 20
We consider the new divisor 154 and the new remainder 20,and apply the division lemma to get
154 = 20 x 7 + 14
We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get
20 = 14 x 1 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 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 8922 and 1178 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(154,20) = HCF(174,154) = HCF(502,174) = HCF(676,502) = HCF(1178,676) = HCF(8922,1178) .
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Frequently Asked Questions on HCF of 8922, 1178 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 8922, 1178?
Answer: HCF of 8922, 1178 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8922, 1178 using Euclid's Algorithm?
Answer: For arbitrary numbers 8922, 1178 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.