Highest Common Factor of 977, 8530 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 977, 8530 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 977, 8530 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 977, 8530 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 977, 8530 is 1.
HCF(977, 8530) = 1
HCF of 977, 8530 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 977, 8530 is 1.
Highest Common Factor of 977,8530 is 1
Step 1: Since 8530 > 977, we apply the division lemma to 8530 and 977, to get
8530 = 977 x 8 + 714
Step 2: Since the reminder 977 ≠ 0, we apply division lemma to 714 and 977, to get
977 = 714 x 1 + 263
Step 3: We consider the new divisor 714 and the new remainder 263, and apply the division lemma to get
714 = 263 x 2 + 188
We consider the new divisor 263 and the new remainder 188,and apply the division lemma to get
263 = 188 x 1 + 75
We consider the new divisor 188 and the new remainder 75,and apply the division lemma to get
188 = 75 x 2 + 38
We consider the new divisor 75 and the new remainder 38,and apply the division lemma to get
75 = 38 x 1 + 37
We consider the new divisor 38 and the new remainder 37,and apply the division lemma to get
38 = 37 x 1 + 1
We consider the new divisor 37 and the new remainder 1,and apply the division lemma to get
37 = 1 x 37 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 977 and 8530 is 1
Notice that 1 = HCF(37,1) = HCF(38,37) = HCF(75,38) = HCF(188,75) = HCF(263,188) = HCF(714,263) = HCF(977,714) = HCF(8530,977) .
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Frequently Asked Questions on HCF of 977, 8530 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 977, 8530?
Answer: HCF of 977, 8530 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 977, 8530 using Euclid's Algorithm?
Answer: For arbitrary numbers 977, 8530 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.