Highest Common Factor of 914, 9720 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 914, 9720 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 914, 9720 is 2 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 914, 9720 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 914, 9720 is 2.
HCF(914, 9720) = 2
HCF of 914, 9720 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 914, 9720 is 2.
Highest Common Factor of 914,9720 is 2
Step 1: Since 9720 > 914, we apply the division lemma to 9720 and 914, to get
9720 = 914 x 10 + 580
Step 2: Since the reminder 914 ≠ 0, we apply division lemma to 580 and 914, to get
914 = 580 x 1 + 334
Step 3: We consider the new divisor 580 and the new remainder 334, and apply the division lemma to get
580 = 334 x 1 + 246
We consider the new divisor 334 and the new remainder 246,and apply the division lemma to get
334 = 246 x 1 + 88
We consider the new divisor 246 and the new remainder 88,and apply the division lemma to get
246 = 88 x 2 + 70
We consider the new divisor 88 and the new remainder 70,and apply the division lemma to get
88 = 70 x 1 + 18
We consider the new divisor 70 and the new remainder 18,and apply the division lemma to get
70 = 18 x 3 + 16
We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get
18 = 16 x 1 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 914 and 9720 is 2
Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(70,18) = HCF(88,70) = HCF(246,88) = HCF(334,246) = HCF(580,334) = HCF(914,580) = HCF(9720,914) .
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Frequently Asked Questions on HCF of 914, 9720 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 914, 9720?
Answer: HCF of 914, 9720 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 914, 9720 using Euclid's Algorithm?
Answer: For arbitrary numbers 914, 9720 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.