Highest Common Factor of 7614, 9022 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 7614, 9022 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 7614, 9022 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 7614, 9022 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 7614, 9022 is 2.
HCF(7614, 9022) = 2
HCF of 7614, 9022 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7614, 9022 is 2.
Highest Common Factor of 7614,9022 is 2
Step 1: Since 9022 > 7614, we apply the division lemma to 9022 and 7614, to get
9022 = 7614 x 1 + 1408
Step 2: Since the reminder 7614 ≠ 0, we apply division lemma to 1408 and 7614, to get
7614 = 1408 x 5 + 574
Step 3: We consider the new divisor 1408 and the new remainder 574, and apply the division lemma to get
1408 = 574 x 2 + 260
We consider the new divisor 574 and the new remainder 260,and apply the division lemma to get
574 = 260 x 2 + 54
We consider the new divisor 260 and the new remainder 54,and apply the division lemma to get
260 = 54 x 4 + 44
We consider the new divisor 54 and the new remainder 44,and apply the division lemma to get
54 = 44 x 1 + 10
We consider the new divisor 44 and the new remainder 10,and apply the division lemma to get
44 = 10 x 4 + 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 7614 and 9022 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(44,10) = HCF(54,44) = HCF(260,54) = HCF(574,260) = HCF(1408,574) = HCF(7614,1408) = HCF(9022,7614) .
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Frequently Asked Questions on HCF of 7614, 9022 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 7614, 9022?
Answer: HCF of 7614, 9022 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7614, 9022 using Euclid's Algorithm?
Answer: For arbitrary numbers 7614, 9022 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.