Highest Common Factor of 401, 674, 77 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 401, 674, 77 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 401, 674, 77 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 401, 674, 77 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 401, 674, 77 is 1.
HCF(401, 674, 77) = 1
HCF of 401, 674, 77 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 401, 674, 77 is 1.
Highest Common Factor of 401,674,77 is 1
Step 1: Since 674 > 401, we apply the division lemma to 674 and 401, to get
674 = 401 x 1 + 273
Step 2: Since the reminder 401 ≠ 0, we apply division lemma to 273 and 401, to get
401 = 273 x 1 + 128
Step 3: We consider the new divisor 273 and the new remainder 128, and apply the division lemma to get
273 = 128 x 2 + 17
We consider the new divisor 128 and the new remainder 17,and apply the division lemma to get
128 = 17 x 7 + 9
We consider the new divisor 17 and the new remainder 9,and apply the division lemma to get
17 = 9 x 1 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 401 and 674 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(17,9) = HCF(128,17) = HCF(273,128) = HCF(401,273) = HCF(674,401) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 77 > 1, we apply the division lemma to 77 and 1, to get
77 = 1 x 77 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 77 is 1
Notice that 1 = HCF(77,1) .
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Frequently Asked Questions on HCF of 401, 674, 77 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 401, 674, 77?
Answer: HCF of 401, 674, 77 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 401, 674, 77 using Euclid's Algorithm?
Answer: For arbitrary numbers 401, 674, 77 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.