Highest Common Factor of 856, 678, 177, 807 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 856, 678, 177, 807 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 856, 678, 177, 807 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 856, 678, 177, 807 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 856, 678, 177, 807 is 1.
HCF(856, 678, 177, 807) = 1
HCF of 856, 678, 177, 807 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 856, 678, 177, 807 is 1.
Highest Common Factor of 856,678,177,807 is 1
Step 1: Since 856 > 678, we apply the division lemma to 856 and 678, to get
856 = 678 x 1 + 178
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 178 and 678, to get
678 = 178 x 3 + 144
Step 3: We consider the new divisor 178 and the new remainder 144, and apply the division lemma to get
178 = 144 x 1 + 34
We consider the new divisor 144 and the new remainder 34,and apply the division lemma to get
144 = 34 x 4 + 8
We consider the new divisor 34 and the new remainder 8,and apply the division lemma to get
34 = 8 x 4 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma 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 856 and 678 is 2
Notice that 2 = HCF(8,2) = HCF(34,8) = HCF(144,34) = HCF(178,144) = HCF(678,178) = HCF(856,678) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 177 > 2, we apply the division lemma to 177 and 2, to get
177 = 2 x 88 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 177 is 1
Notice that 1 = HCF(2,1) = HCF(177,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 807 > 1, we apply the division lemma to 807 and 1, to get
807 = 1 x 807 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 807 is 1
Notice that 1 = HCF(807,1) .
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Frequently Asked Questions on HCF of 856, 678, 177, 807 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 856, 678, 177, 807?
Answer: HCF of 856, 678, 177, 807 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 856, 678, 177, 807 using Euclid's Algorithm?
Answer: For arbitrary numbers 856, 678, 177, 807 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.