Highest Common Factor of 996, 69440 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, 69440 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 996, 69440 is 4 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, 69440 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, 69440 is 4.
HCF(996, 69440) = 4
HCF of 996, 69440 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, 69440 is 4.
Highest Common Factor of 996,69440 is 4
Step 1: Since 69440 > 996, we apply the division lemma to 69440 and 996, to get
69440 = 996 x 69 + 716
Step 2: Since the reminder 996 ≠ 0, we apply division lemma to 716 and 996, to get
996 = 716 x 1 + 280
Step 3: We consider the new divisor 716 and the new remainder 280, and apply the division lemma to get
716 = 280 x 2 + 156
We consider the new divisor 280 and the new remainder 156,and apply the division lemma to get
280 = 156 x 1 + 124
We consider the new divisor 156 and the new remainder 124,and apply the division lemma to get
156 = 124 x 1 + 32
We consider the new divisor 124 and the new remainder 32,and apply the division lemma to get
124 = 32 x 3 + 28
We consider the new divisor 32 and the new remainder 28,and apply the division lemma to get
32 = 28 x 1 + 4
We consider the new divisor 28 and the new remainder 4,and apply the division lemma to get
28 = 4 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 996 and 69440 is 4
Notice that 4 = HCF(28,4) = HCF(32,28) = HCF(124,32) = HCF(156,124) = HCF(280,156) = HCF(716,280) = HCF(996,716) = HCF(69440,996) .
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Frequently Asked Questions on HCF of 996, 69440 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, 69440?
Answer: HCF of 996, 69440 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 996, 69440 using Euclid's Algorithm?
Answer: For arbitrary numbers 996, 69440 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.