Highest Common Factor of 678, 775, 472 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, 775, 472 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 775, 472 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 678, 775, 472 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, 775, 472 is 1.
HCF(678, 775, 472) = 1
HCF of 678, 775, 472 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, 775, 472 is 1.
Highest Common Factor of 678,775,472 is 1
Step 1: Since 775 > 678, we apply the division lemma to 775 and 678, to get
775 = 678 x 1 + 97
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 97 and 678, to get
678 = 97 x 6 + 96
Step 3: We consider the new divisor 97 and the new remainder 96, and apply the division lemma to get
97 = 96 x 1 + 1
We consider the new divisor 96 and the new remainder 1, and apply the division lemma to get
96 = 1 x 96 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 678 and 775 is 1
Notice that 1 = HCF(96,1) = HCF(97,96) = HCF(678,97) = HCF(775,678) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 472 > 1, we apply the division lemma to 472 and 1, to get
472 = 1 x 472 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 472 is 1
Notice that 1 = HCF(472,1) .
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Frequently Asked Questions on HCF of 678, 775, 472 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, 775, 472?
Answer: HCF of 678, 775, 472 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 775, 472 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 775, 472 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
