Highest Common Factor of 7680, 8900 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 7680, 8900 i.e. 20 the largest integer that leaves a remainder zero for all numbers.
HCF of 7680, 8900 is 20 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 7680, 8900 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 7680, 8900 is 20.
HCF(7680, 8900) = 20
HCF of 7680, 8900 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7680, 8900 is 20.
Highest Common Factor of 7680,8900 is 20
Step 1: Since 8900 > 7680, we apply the division lemma to 8900 and 7680, to get
8900 = 7680 x 1 + 1220
Step 2: Since the reminder 7680 ≠ 0, we apply division lemma to 1220 and 7680, to get
7680 = 1220 x 6 + 360
Step 3: We consider the new divisor 1220 and the new remainder 360, and apply the division lemma to get
1220 = 360 x 3 + 140
We consider the new divisor 360 and the new remainder 140,and apply the division lemma to get
360 = 140 x 2 + 80
We consider the new divisor 140 and the new remainder 80,and apply the division lemma to get
140 = 80 x 1 + 60
We consider the new divisor 80 and the new remainder 60,and apply the division lemma to get
80 = 60 x 1 + 20
We consider the new divisor 60 and the new remainder 20,and apply the division lemma to get
60 = 20 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 7680 and 8900 is 20
Notice that 20 = HCF(60,20) = HCF(80,60) = HCF(140,80) = HCF(360,140) = HCF(1220,360) = HCF(7680,1220) = HCF(8900,7680) .
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Frequently Asked Questions on HCF of 7680, 8900 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 7680, 8900?
Answer: HCF of 7680, 8900 is 20 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7680, 8900 using Euclid's Algorithm?
Answer: For arbitrary numbers 7680, 8900 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
