Highest Common Factor of 896, 7670 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 896, 7670 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 896, 7670 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 896, 7670 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 896, 7670 is 2.
HCF(896, 7670) = 2
HCF of 896, 7670 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 896, 7670 is 2.
Highest Common Factor of 896,7670 is 2
Step 1: Since 7670 > 896, we apply the division lemma to 7670 and 896, to get
7670 = 896 x 8 + 502
Step 2: Since the reminder 896 ≠ 0, we apply division lemma to 502 and 896, to get
896 = 502 x 1 + 394
Step 3: We consider the new divisor 502 and the new remainder 394, and apply the division lemma to get
502 = 394 x 1 + 108
We consider the new divisor 394 and the new remainder 108,and apply the division lemma to get
394 = 108 x 3 + 70
We consider the new divisor 108 and the new remainder 70,and apply the division lemma to get
108 = 70 x 1 + 38
We consider the new divisor 70 and the new remainder 38,and apply the division lemma to get
70 = 38 x 1 + 32
We consider the new divisor 38 and the new remainder 32,and apply the division lemma to get
38 = 32 x 1 + 6
We consider the new divisor 32 and the new remainder 6,and apply the division lemma to get
32 = 6 x 5 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 896 and 7670 is 2
Notice that 2 = HCF(6,2) = HCF(32,6) = HCF(38,32) = HCF(70,38) = HCF(108,70) = HCF(394,108) = HCF(502,394) = HCF(896,502) = HCF(7670,896) .
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Frequently Asked Questions on HCF of 896, 7670 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 896, 7670?
Answer: HCF of 896, 7670 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 896, 7670 using Euclid's Algorithm?
Answer: For arbitrary numbers 896, 7670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.