Highest Common Factor of 278, 61123 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 278, 61123 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 278, 61123 is 1 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 278, 61123 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 278, 61123 is 1.
HCF(278, 61123) = 1
HCF of 278, 61123 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 278, 61123 is 1.
Highest Common Factor of 278,61123 is 1
Step 1: Since 61123 > 278, we apply the division lemma to 61123 and 278, to get
61123 = 278 x 219 + 241
Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 241 and 278, to get
278 = 241 x 1 + 37
Step 3: We consider the new divisor 241 and the new remainder 37, and apply the division lemma to get
241 = 37 x 6 + 19
We consider the new divisor 37 and the new remainder 19,and apply the division lemma to get
37 = 19 x 1 + 18
We consider the new divisor 19 and the new remainder 18,and apply the division lemma to get
19 = 18 x 1 + 1
We consider the new divisor 18 and the new remainder 1,and apply the division lemma to get
18 = 1 x 18 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 278 and 61123 is 1
Notice that 1 = HCF(18,1) = HCF(19,18) = HCF(37,19) = HCF(241,37) = HCF(278,241) = HCF(61123,278) .
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Frequently Asked Questions on HCF of 278, 61123 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 278, 61123?
Answer: HCF of 278, 61123 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 278, 61123 using Euclid's Algorithm?
Answer: For arbitrary numbers 278, 61123 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.