Highest Common Factor of 278, 492, 916 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, 492, 916 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 278, 492, 916 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 278, 492, 916 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, 492, 916 is 2.
HCF(278, 492, 916) = 2
HCF of 278, 492, 916 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, 492, 916 is 2.
Highest Common Factor of 278,492,916 is 2
Step 1: Since 492 > 278, we apply the division lemma to 492 and 278, to get
492 = 278 x 1 + 214
Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 214 and 278, to get
278 = 214 x 1 + 64
Step 3: We consider the new divisor 214 and the new remainder 64, and apply the division lemma to get
214 = 64 x 3 + 22
We consider the new divisor 64 and the new remainder 22,and apply the division lemma to get
64 = 22 x 2 + 20
We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get
22 = 20 x 1 + 2
We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get
20 = 2 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 278 and 492 is 2
Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(64,22) = HCF(214,64) = HCF(278,214) = HCF(492,278) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 916 > 2, we apply the division lemma to 916 and 2, to get
916 = 2 x 458 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 916 is 2
Notice that 2 = HCF(916,2) .
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Frequently Asked Questions on HCF of 278, 492, 916 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, 492, 916?
Answer: HCF of 278, 492, 916 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 278, 492, 916 using Euclid's Algorithm?
Answer: For arbitrary numbers 278, 492, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.