Highest Common Factor of 616, 966 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 616, 966 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 616, 966 is 14 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 616, 966 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 616, 966 is 14.
HCF(616, 966) = 14
HCF of 616, 966 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 616, 966 is 14.
Highest Common Factor of 616,966 is 14
Step 1: Since 966 > 616, we apply the division lemma to 966 and 616, to get
966 = 616 x 1 + 350
Step 2: Since the reminder 616 ≠ 0, we apply division lemma to 350 and 616, to get
616 = 350 x 1 + 266
Step 3: We consider the new divisor 350 and the new remainder 266, and apply the division lemma to get
350 = 266 x 1 + 84
We consider the new divisor 266 and the new remainder 84,and apply the division lemma to get
266 = 84 x 3 + 14
We consider the new divisor 84 and the new remainder 14,and apply the division lemma to get
84 = 14 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 616 and 966 is 14
Notice that 14 = HCF(84,14) = HCF(266,84) = HCF(350,266) = HCF(616,350) = HCF(966,616) .
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Frequently Asked Questions on HCF of 616, 966 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 616, 966?
Answer: HCF of 616, 966 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 616, 966 using Euclid's Algorithm?
Answer: For arbitrary numbers 616, 966 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.