Highest Common Factor of 235, 856, 974 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 235, 856, 974 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 235, 856, 974 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 235, 856, 974 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 235, 856, 974 is 1.
HCF(235, 856, 974) = 1
HCF of 235, 856, 974 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 235, 856, 974 is 1.
Highest Common Factor of 235,856,974 is 1
Step 1: Since 856 > 235, we apply the division lemma to 856 and 235, to get
856 = 235 x 3 + 151
Step 2: Since the reminder 235 ≠ 0, we apply division lemma to 151 and 235, to get
235 = 151 x 1 + 84
Step 3: We consider the new divisor 151 and the new remainder 84, and apply the division lemma to get
151 = 84 x 1 + 67
We consider the new divisor 84 and the new remainder 67,and apply the division lemma to get
84 = 67 x 1 + 17
We consider the new divisor 67 and the new remainder 17,and apply the division lemma to get
67 = 17 x 3 + 16
We consider the new divisor 17 and the new remainder 16,and apply the division lemma to get
17 = 16 x 1 + 1
We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 235 and 856 is 1
Notice that 1 = HCF(16,1) = HCF(17,16) = HCF(67,17) = HCF(84,67) = HCF(151,84) = HCF(235,151) = HCF(856,235) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 974 > 1, we apply the division lemma to 974 and 1, to get
974 = 1 x 974 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 974 is 1
Notice that 1 = HCF(974,1) .
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Frequently Asked Questions on HCF of 235, 856, 974 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 235, 856, 974?
Answer: HCF of 235, 856, 974 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 235, 856, 974 using Euclid's Algorithm?
Answer: For arbitrary numbers 235, 856, 974 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.