Highest Common Factor of 996, 655 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 996, 655 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 996, 655 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 996, 655 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 996, 655 is 1.
HCF(996, 655) = 1
HCF of 996, 655 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 996, 655 is 1.
Highest Common Factor of 996,655 is 1
Step 1: Since 996 > 655, we apply the division lemma to 996 and 655, to get
996 = 655 x 1 + 341
Step 2: Since the reminder 655 ≠ 0, we apply division lemma to 341 and 655, to get
655 = 341 x 1 + 314
Step 3: We consider the new divisor 341 and the new remainder 314, and apply the division lemma to get
341 = 314 x 1 + 27
We consider the new divisor 314 and the new remainder 27,and apply the division lemma to get
314 = 27 x 11 + 17
We consider the new divisor 27 and the new remainder 17,and apply the division lemma to get
27 = 17 x 1 + 10
We consider the new divisor 17 and the new remainder 10,and apply the division lemma to get
17 = 10 x 1 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 996 and 655 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(17,10) = HCF(27,17) = HCF(314,27) = HCF(341,314) = HCF(655,341) = HCF(996,655) .
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Frequently Asked Questions on HCF of 996, 655 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 996, 655?
Answer: HCF of 996, 655 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 996, 655 using Euclid's Algorithm?
Answer: For arbitrary numbers 996, 655 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.