Highest Common Factor of 678, 904, 565 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 678, 904, 565 i.e. 113 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 904, 565 is 113 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 678, 904, 565 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 678, 904, 565 is 113.
HCF(678, 904, 565) = 113
HCF of 678, 904, 565 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 904, 565 is 113.
Highest Common Factor of 678,904,565 is 113
Step 1: Since 904 > 678, we apply the division lemma to 904 and 678, to get
904 = 678 x 1 + 226
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 226 and 678, to get
678 = 226 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 226, the HCF of 678 and 904 is 226
Notice that 226 = HCF(678,226) = HCF(904,678) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 565 > 226, we apply the division lemma to 565 and 226, to get
565 = 226 x 2 + 113
Step 2: Since the reminder 226 ≠ 0, we apply division lemma to 113 and 226, to get
226 = 113 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 113, the HCF of 226 and 565 is 113
Notice that 113 = HCF(226,113) = HCF(565,226) .
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Frequently Asked Questions on HCF of 678, 904, 565 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 678, 904, 565?
Answer: HCF of 678, 904, 565 is 113 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 904, 565 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 904, 565 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.