Highest Common Factor of 616, 7282 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 616, 7282 i.e. 22 the largest integer that leaves a remainder zero for all numbers.
HCF of 616, 7282 is 22 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 616, 7282 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 616, 7282 is 22.
HCF(616, 7282) = 22
HCF of 616, 7282 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 616, 7282 is 22.
Highest Common Factor of 616,7282 is 22
Step 1: Since 7282 > 616, we apply the division lemma to 7282 and 616, to get
7282 = 616 x 11 + 506
Step 2: Since the reminder 616 ≠ 0, we apply division lemma to 506 and 616, to get
616 = 506 x 1 + 110
Step 3: We consider the new divisor 506 and the new remainder 110, and apply the division lemma to get
506 = 110 x 4 + 66
We consider the new divisor 110 and the new remainder 66,and apply the division lemma to get
110 = 66 x 1 + 44
We consider the new divisor 66 and the new remainder 44,and apply the division lemma to get
66 = 44 x 1 + 22
We consider the new divisor 44 and the new remainder 22,and apply the division lemma to get
44 = 22 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 22, the HCF of 616 and 7282 is 22
Notice that 22 = HCF(44,22) = HCF(66,44) = HCF(110,66) = HCF(506,110) = HCF(616,506) = HCF(7282,616) .
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Frequently Asked Questions on HCF of 616, 7282 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 616, 7282?
Answer: HCF of 616, 7282 is 22 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 616, 7282 using Euclid's Algorithm?
Answer: For arbitrary numbers 616, 7282 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.