Highest Common Factor of 301, 770, 188 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 301, 770, 188 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 301, 770, 188 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 301, 770, 188 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 301, 770, 188 is 1.
HCF(301, 770, 188) = 1
HCF of 301, 770, 188 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 301, 770, 188 is 1.
Highest Common Factor of 301,770,188 is 1
Step 1: Since 770 > 301, we apply the division lemma to 770 and 301, to get
770 = 301 x 2 + 168
Step 2: Since the reminder 301 ≠ 0, we apply division lemma to 168 and 301, to get
301 = 168 x 1 + 133
Step 3: We consider the new divisor 168 and the new remainder 133, and apply the division lemma to get
168 = 133 x 1 + 35
We consider the new divisor 133 and the new remainder 35,and apply the division lemma to get
133 = 35 x 3 + 28
We consider the new divisor 35 and the new remainder 28,and apply the division lemma to get
35 = 28 x 1 + 7
We consider the new divisor 28 and the new remainder 7,and apply the division lemma to get
28 = 7 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 301 and 770 is 7
Notice that 7 = HCF(28,7) = HCF(35,28) = HCF(133,35) = HCF(168,133) = HCF(301,168) = HCF(770,301) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 188 > 7, we apply the division lemma to 188 and 7, to get
188 = 7 x 26 + 6
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 6 and 7, to get
7 = 6 x 1 + 1
Step 3: We consider the new divisor 6 and the new remainder 1, and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 188 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(188,7) .
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Frequently Asked Questions on HCF of 301, 770, 188 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 301, 770, 188?
Answer: HCF of 301, 770, 188 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 301, 770, 188 using Euclid's Algorithm?
Answer: For arbitrary numbers 301, 770, 188 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.