Highest Common Factor of 610, 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 610, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 610, 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 610, 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 610, 977 is 1.
HCF(610, 977) = 1
HCF of 610, 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 610, 977 is 1.
Highest Common Factor of 610,977 is 1
Step 1: Since 977 > 610, we apply the division lemma to 977 and 610, to get
977 = 610 x 1 + 367
Step 2: Since the reminder 610 ≠ 0, we apply division lemma to 367 and 610, to get
610 = 367 x 1 + 243
Step 3: We consider the new divisor 367 and the new remainder 243, and apply the division lemma to get
367 = 243 x 1 + 124
We consider the new divisor 243 and the new remainder 124,and apply the division lemma to get
243 = 124 x 1 + 119
We consider the new divisor 124 and the new remainder 119,and apply the division lemma to get
124 = 119 x 1 + 5
We consider the new divisor 119 and the new remainder 5,and apply the division lemma to get
119 = 5 x 23 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 610 and 977 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(119,5) = HCF(124,119) = HCF(243,124) = HCF(367,243) = HCF(610,367) = HCF(977,610) .
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Frequently Asked Questions on HCF of 610, 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 610, 977?
Answer: HCF of 610, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 610, 977 using Euclid's Algorithm?
Answer: For arbitrary numbers 610, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
