Highest Common Factor of 760, 200, 177 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 760, 200, 177 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 760, 200, 177 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 760, 200, 177 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 760, 200, 177 is 1.
HCF(760, 200, 177) = 1
HCF of 760, 200, 177 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 760, 200, 177 is 1.
Highest Common Factor of 760,200,177 is 1
Step 1: Since 760 > 200, we apply the division lemma to 760 and 200, to get
760 = 200 x 3 + 160
Step 2: Since the reminder 200 ≠ 0, we apply division lemma to 160 and 200, to get
200 = 160 x 1 + 40
Step 3: We consider the new divisor 160 and the new remainder 40, and apply the division lemma to get
160 = 40 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 760 and 200 is 40
Notice that 40 = HCF(160,40) = HCF(200,160) = HCF(760,200) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 177 > 40, we apply the division lemma to 177 and 40, to get
177 = 40 x 4 + 17
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 17 and 40, to get
40 = 17 x 2 + 6
Step 3: We consider the new divisor 17 and the new remainder 6, and apply the division lemma to get
17 = 6 x 2 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 40 and 177 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(40,17) = HCF(177,40) .
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Frequently Asked Questions on HCF of 760, 200, 177 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 760, 200, 177?
Answer: HCF of 760, 200, 177 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 760, 200, 177 using Euclid's Algorithm?
Answer: For arbitrary numbers 760, 200, 177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.