Highest Common Factor of 721, 455, 616, 977 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 721, 455, 616, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 721, 455, 616, 977 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 721, 455, 616, 977 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 721, 455, 616, 977 is 1.
HCF(721, 455, 616, 977) = 1
HCF of 721, 455, 616, 977 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 721, 455, 616, 977 is 1.
Highest Common Factor of 721,455,616,977 is 1
Step 1: Since 721 > 455, we apply the division lemma to 721 and 455, to get
721 = 455 x 1 + 266
Step 2: Since the reminder 455 ≠ 0, we apply division lemma to 266 and 455, to get
455 = 266 x 1 + 189
Step 3: We consider the new divisor 266 and the new remainder 189, and apply the division lemma to get
266 = 189 x 1 + 77
We consider the new divisor 189 and the new remainder 77,and apply the division lemma to get
189 = 77 x 2 + 35
We consider the new divisor 77 and the new remainder 35,and apply the division lemma to get
77 = 35 x 2 + 7
We consider the new divisor 35 and the new remainder 7,and apply the division lemma to get
35 = 7 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 721 and 455 is 7
Notice that 7 = HCF(35,7) = HCF(77,35) = HCF(189,77) = HCF(266,189) = HCF(455,266) = HCF(721,455) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 616 > 7, we apply the division lemma to 616 and 7, to get
616 = 7 x 88 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 7 and 616 is 7
Notice that 7 = HCF(616,7) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 977 > 7, we apply the division lemma to 977 and 7, to get
977 = 7 x 139 + 4
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 4 and 7, to get
7 = 4 x 1 + 3
Step 3: We consider the new divisor 4 and the new remainder 3, and apply the division lemma to get
4 = 3 x 1 + 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 7 and 977 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(977,7) .
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Frequently Asked Questions on HCF of 721, 455, 616, 977 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 721, 455, 616, 977?
Answer: HCF of 721, 455, 616, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 721, 455, 616, 977 using Euclid's Algorithm?
Answer: For arbitrary numbers 721, 455, 616, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.