Highest Common Factor of 6954, 9172 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 6954, 9172 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6954, 9172 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 6954, 9172 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 6954, 9172 is 2.
HCF(6954, 9172) = 2
HCF of 6954, 9172 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6954, 9172 is 2.
Highest Common Factor of 6954,9172 is 2
Step 1: Since 9172 > 6954, we apply the division lemma to 9172 and 6954, to get
9172 = 6954 x 1 + 2218
Step 2: Since the reminder 6954 ≠ 0, we apply division lemma to 2218 and 6954, to get
6954 = 2218 x 3 + 300
Step 3: We consider the new divisor 2218 and the new remainder 300, and apply the division lemma to get
2218 = 300 x 7 + 118
We consider the new divisor 300 and the new remainder 118,and apply the division lemma to get
300 = 118 x 2 + 64
We consider the new divisor 118 and the new remainder 64,and apply the division lemma to get
118 = 64 x 1 + 54
We consider the new divisor 64 and the new remainder 54,and apply the division lemma to get
64 = 54 x 1 + 10
We consider the new divisor 54 and the new remainder 10,and apply the division lemma to get
54 = 10 x 5 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6954 and 9172 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(54,10) = HCF(64,54) = HCF(118,64) = HCF(300,118) = HCF(2218,300) = HCF(6954,2218) = HCF(9172,6954) .
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Frequently Asked Questions on HCF of 6954, 9172 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 6954, 9172?
Answer: HCF of 6954, 9172 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6954, 9172 using Euclid's Algorithm?
Answer: For arbitrary numbers 6954, 9172 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.