Highest Common Factor of 920, 584, 378 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 920, 584, 378 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 920, 584, 378 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 920, 584, 378 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 920, 584, 378 is 2.
HCF(920, 584, 378) = 2
HCF of 920, 584, 378 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 920, 584, 378 is 2.
Highest Common Factor of 920,584,378 is 2
Step 1: Since 920 > 584, we apply the division lemma to 920 and 584, to get
920 = 584 x 1 + 336
Step 2: Since the reminder 584 ≠ 0, we apply division lemma to 336 and 584, to get
584 = 336 x 1 + 248
Step 3: We consider the new divisor 336 and the new remainder 248, and apply the division lemma to get
336 = 248 x 1 + 88
We consider the new divisor 248 and the new remainder 88,and apply the division lemma to get
248 = 88 x 2 + 72
We consider the new divisor 88 and the new remainder 72,and apply the division lemma to get
88 = 72 x 1 + 16
We consider the new divisor 72 and the new remainder 16,and apply the division lemma to get
72 = 16 x 4 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 920 and 584 is 8
Notice that 8 = HCF(16,8) = HCF(72,16) = HCF(88,72) = HCF(248,88) = HCF(336,248) = HCF(584,336) = HCF(920,584) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 378 > 8, we apply the division lemma to 378 and 8, to get
378 = 8 x 47 + 2
Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 2 and 8, to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8 and 378 is 2
Notice that 2 = HCF(8,2) = HCF(378,8) .
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Frequently Asked Questions on HCF of 920, 584, 378 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 920, 584, 378?
Answer: HCF of 920, 584, 378 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 920, 584, 378 using Euclid's Algorithm?
Answer: For arbitrary numbers 920, 584, 378 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.