Highest Common Factor of 2220, 7137 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 2220, 7137 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2220, 7137 is 3 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 2220, 7137 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 2220, 7137 is 3.
HCF(2220, 7137) = 3
HCF of 2220, 7137 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2220, 7137 is 3.
Highest Common Factor of 2220,7137 is 3
Step 1: Since 7137 > 2220, we apply the division lemma to 7137 and 2220, to get
7137 = 2220 x 3 + 477
Step 2: Since the reminder 2220 ≠ 0, we apply division lemma to 477 and 2220, to get
2220 = 477 x 4 + 312
Step 3: We consider the new divisor 477 and the new remainder 312, and apply the division lemma to get
477 = 312 x 1 + 165
We consider the new divisor 312 and the new remainder 165,and apply the division lemma to get
312 = 165 x 1 + 147
We consider the new divisor 165 and the new remainder 147,and apply the division lemma to get
165 = 147 x 1 + 18
We consider the new divisor 147 and the new remainder 18,and apply the division lemma to get
147 = 18 x 8 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2220 and 7137 is 3
Notice that 3 = HCF(18,3) = HCF(147,18) = HCF(165,147) = HCF(312,165) = HCF(477,312) = HCF(2220,477) = HCF(7137,2220) .
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Frequently Asked Questions on HCF of 2220, 7137 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 2220, 7137?
Answer: HCF of 2220, 7137 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2220, 7137 using Euclid's Algorithm?
Answer: For arbitrary numbers 2220, 7137 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.