Highest Common Factor of 977, 128 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, 128 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 977, 128 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, 128 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, 128 is 1.
HCF(977, 128) = 1
HCF of 977, 128 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, 128 is 1.
Highest Common Factor of 977,128 is 1
Step 1: Since 977 > 128, we apply the division lemma to 977 and 128, to get
977 = 128 x 7 + 81
Step 2: Since the reminder 128 ≠ 0, we apply division lemma to 81 and 128, to get
128 = 81 x 1 + 47
Step 3: We consider the new divisor 81 and the new remainder 47, and apply the division lemma to get
81 = 47 x 1 + 34
We consider the new divisor 47 and the new remainder 34,and apply the division lemma to get
47 = 34 x 1 + 13
We consider the new divisor 34 and the new remainder 13,and apply the division lemma to get
34 = 13 x 2 + 8
We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get
13 = 8 x 1 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 977 and 128 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(34,13) = HCF(47,34) = HCF(81,47) = HCF(128,81) = HCF(977,128) .
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Frequently Asked Questions on HCF of 977, 128 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, 128?
Answer: HCF of 977, 128 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 977, 128 using Euclid's Algorithm?
Answer: For arbitrary numbers 977, 128 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.