Highest Common Factor of 722, 278 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 722, 278 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 722, 278 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 722, 278 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 722, 278 is 2.
HCF(722, 278) = 2
HCF of 722, 278 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 722, 278 is 2.
Highest Common Factor of 722,278 is 2
Step 1: Since 722 > 278, we apply the division lemma to 722 and 278, to get
722 = 278 x 2 + 166
Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 166 and 278, to get
278 = 166 x 1 + 112
Step 3: We consider the new divisor 166 and the new remainder 112, and apply the division lemma to get
166 = 112 x 1 + 54
We consider the new divisor 112 and the new remainder 54,and apply the division lemma to get
112 = 54 x 2 + 4
We consider the new divisor 54 and the new remainder 4,and apply the division lemma to get
54 = 4 x 13 + 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 722 and 278 is 2
Notice that 2 = HCF(4,2) = HCF(54,4) = HCF(112,54) = HCF(166,112) = HCF(278,166) = HCF(722,278) .
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Frequently Asked Questions on HCF of 722, 278 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 722, 278?
Answer: HCF of 722, 278 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 722, 278 using Euclid's Algorithm?
Answer: For arbitrary numbers 722, 278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.