Highest Common Factor of 529, 988, 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 529, 988, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 529, 988, 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 529, 988, 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 529, 988, 977 is 1.
HCF(529, 988, 977) = 1
HCF of 529, 988, 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 529, 988, 977 is 1.
Highest Common Factor of 529,988,977 is 1
Step 1: Since 988 > 529, we apply the division lemma to 988 and 529, to get
988 = 529 x 1 + 459
Step 2: Since the reminder 529 ≠ 0, we apply division lemma to 459 and 529, to get
529 = 459 x 1 + 70
Step 3: We consider the new divisor 459 and the new remainder 70, and apply the division lemma to get
459 = 70 x 6 + 39
We consider the new divisor 70 and the new remainder 39,and apply the division lemma to get
70 = 39 x 1 + 31
We consider the new divisor 39 and the new remainder 31,and apply the division lemma to get
39 = 31 x 1 + 8
We consider the new divisor 31 and the new remainder 8,and apply the division lemma to get
31 = 8 x 3 + 7
We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get
8 = 7 x 1 + 1
We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 529 and 988 is 1
Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(31,8) = HCF(39,31) = HCF(70,39) = HCF(459,70) = HCF(529,459) = HCF(988,529) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 977 > 1, we apply the division lemma to 977 and 1, to get
977 = 1 x 977 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 977 is 1
Notice that 1 = HCF(977,1) .
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Frequently Asked Questions on HCF of 529, 988, 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 529, 988, 977?
Answer: HCF of 529, 988, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 529, 988, 977 using Euclid's Algorithm?
Answer: For arbitrary numbers 529, 988, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.