Highest Common Factor of 298, 735, 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 298, 735, 278 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 298, 735, 278 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 298, 735, 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 298, 735, 278 is 1.
HCF(298, 735, 278) = 1
HCF of 298, 735, 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 298, 735, 278 is 1.
Highest Common Factor of 298,735,278 is 1
Step 1: Since 735 > 298, we apply the division lemma to 735 and 298, to get
735 = 298 x 2 + 139
Step 2: Since the reminder 298 ≠ 0, we apply division lemma to 139 and 298, to get
298 = 139 x 2 + 20
Step 3: We consider the new divisor 139 and the new remainder 20, and apply the division lemma to get
139 = 20 x 6 + 19
We consider the new divisor 20 and the new remainder 19,and apply the division lemma to get
20 = 19 x 1 + 1
We consider the new divisor 19 and the new remainder 1,and apply the division lemma to get
19 = 1 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 298 and 735 is 1
Notice that 1 = HCF(19,1) = HCF(20,19) = HCF(139,20) = HCF(298,139) = HCF(735,298) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 278 > 1, we apply the division lemma to 278 and 1, to get
278 = 1 x 278 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 278 is 1
Notice that 1 = HCF(278,1) .
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Frequently Asked Questions on HCF of 298, 735, 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 298, 735, 278?
Answer: HCF of 298, 735, 278 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 298, 735, 278 using Euclid's Algorithm?
Answer: For arbitrary numbers 298, 735, 278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
