Highest Common Factor of 976, 7973 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 976, 7973 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 976, 7973 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 976, 7973 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 976, 7973 is 1.
HCF(976, 7973) = 1
HCF of 976, 7973 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 976, 7973 is 1.
Highest Common Factor of 976,7973 is 1
Step 1: Since 7973 > 976, we apply the division lemma to 7973 and 976, to get
7973 = 976 x 8 + 165
Step 2: Since the reminder 976 ≠ 0, we apply division lemma to 165 and 976, to get
976 = 165 x 5 + 151
Step 3: We consider the new divisor 165 and the new remainder 151, and apply the division lemma to get
165 = 151 x 1 + 14
We consider the new divisor 151 and the new remainder 14,and apply the division lemma to get
151 = 14 x 10 + 11
We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get
14 = 11 x 1 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 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 976 and 7973 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(151,14) = HCF(165,151) = HCF(976,165) = HCF(7973,976) .
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Frequently Asked Questions on HCF of 976, 7973 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 976, 7973?
Answer: HCF of 976, 7973 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 976, 7973 using Euclid's Algorithm?
Answer: For arbitrary numbers 976, 7973 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.