Highest Common Factor of 857, 668, 169, 72 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 857, 668, 169, 72 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 857, 668, 169, 72 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 857, 668, 169, 72 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 857, 668, 169, 72 is 1.
HCF(857, 668, 169, 72) = 1
HCF of 857, 668, 169, 72 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 857, 668, 169, 72 is 1.
Highest Common Factor of 857,668,169,72 is 1
Step 1: Since 857 > 668, we apply the division lemma to 857 and 668, to get
857 = 668 x 1 + 189
Step 2: Since the reminder 668 ≠ 0, we apply division lemma to 189 and 668, to get
668 = 189 x 3 + 101
Step 3: We consider the new divisor 189 and the new remainder 101, and apply the division lemma to get
189 = 101 x 1 + 88
We consider the new divisor 101 and the new remainder 88,and apply the division lemma to get
101 = 88 x 1 + 13
We consider the new divisor 88 and the new remainder 13,and apply the division lemma to get
88 = 13 x 6 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 857 and 668 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(88,13) = HCF(101,88) = HCF(189,101) = HCF(668,189) = HCF(857,668) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 169 > 1, we apply the division lemma to 169 and 1, to get
169 = 1 x 169 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 169 is 1
Notice that 1 = HCF(169,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 72 > 1, we apply the division lemma to 72 and 1, to get
72 = 1 x 72 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 72 is 1
Notice that 1 = HCF(72,1) .
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Frequently Asked Questions on HCF of 857, 668, 169, 72 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 857, 668, 169, 72?
Answer: HCF of 857, 668, 169, 72 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 857, 668, 169, 72 using Euclid's Algorithm?
Answer: For arbitrary numbers 857, 668, 169, 72 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.