Highest Common Factor of 661, 8978 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 661, 8978 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 661, 8978 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 661, 8978 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 661, 8978 is 1.
HCF(661, 8978) = 1
HCF of 661, 8978 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 661, 8978 is 1.
Highest Common Factor of 661,8978 is 1
Step 1: Since 8978 > 661, we apply the division lemma to 8978 and 661, to get
8978 = 661 x 13 + 385
Step 2: Since the reminder 661 ≠ 0, we apply division lemma to 385 and 661, to get
661 = 385 x 1 + 276
Step 3: We consider the new divisor 385 and the new remainder 276, and apply the division lemma to get
385 = 276 x 1 + 109
We consider the new divisor 276 and the new remainder 109,and apply the division lemma to get
276 = 109 x 2 + 58
We consider the new divisor 109 and the new remainder 58,and apply the division lemma to get
109 = 58 x 1 + 51
We consider the new divisor 58 and the new remainder 51,and apply the division lemma to get
58 = 51 x 1 + 7
We consider the new divisor 51 and the new remainder 7,and apply the division lemma to get
51 = 7 x 7 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 661 and 8978 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(51,7) = HCF(58,51) = HCF(109,58) = HCF(276,109) = HCF(385,276) = HCF(661,385) = HCF(8978,661) .
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Frequently Asked Questions on HCF of 661, 8978 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 661, 8978?
Answer: HCF of 661, 8978 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 661, 8978 using Euclid's Algorithm?
Answer: For arbitrary numbers 661, 8978 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.