Highest Common Factor of 102, 851, 380 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 102, 851, 380 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 102, 851, 380 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 102, 851, 380 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 102, 851, 380 is 1.
HCF(102, 851, 380) = 1
HCF of 102, 851, 380 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 102, 851, 380 is 1.
Highest Common Factor of 102,851,380 is 1
Step 1: Since 851 > 102, we apply the division lemma to 851 and 102, to get
851 = 102 x 8 + 35
Step 2: Since the reminder 102 ≠ 0, we apply division lemma to 35 and 102, to get
102 = 35 x 2 + 32
Step 3: We consider the new divisor 35 and the new remainder 32, and apply the division lemma to get
35 = 32 x 1 + 3
We consider the new divisor 32 and the new remainder 3,and apply the division lemma to get
32 = 3 x 10 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 102 and 851 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(32,3) = HCF(35,32) = HCF(102,35) = HCF(851,102) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 380 > 1, we apply the division lemma to 380 and 1, to get
380 = 1 x 380 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 380 is 1
Notice that 1 = HCF(380,1) .
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Frequently Asked Questions on HCF of 102, 851, 380 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 102, 851, 380?
Answer: HCF of 102, 851, 380 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 102, 851, 380 using Euclid's Algorithm?
Answer: For arbitrary numbers 102, 851, 380 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.