Highest Common Factor of 770, 7802 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 770, 7802 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 770, 7802 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 770, 7802 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 770, 7802 is 2.
HCF(770, 7802) = 2
HCF of 770, 7802 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 770, 7802 is 2.
Highest Common Factor of 770,7802 is 2
Step 1: Since 7802 > 770, we apply the division lemma to 7802 and 770, to get
7802 = 770 x 10 + 102
Step 2: Since the reminder 770 ≠ 0, we apply division lemma to 102 and 770, to get
770 = 102 x 7 + 56
Step 3: We consider the new divisor 102 and the new remainder 56, and apply the division lemma to get
102 = 56 x 1 + 46
We consider the new divisor 56 and the new remainder 46,and apply the division lemma to get
56 = 46 x 1 + 10
We consider the new divisor 46 and the new remainder 10,and apply the division lemma to get
46 = 10 x 4 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 770 and 7802 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(46,10) = HCF(56,46) = HCF(102,56) = HCF(770,102) = HCF(7802,770) .
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Frequently Asked Questions on HCF of 770, 7802 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 770, 7802?
Answer: HCF of 770, 7802 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 770, 7802 using Euclid's Algorithm?
Answer: For arbitrary numbers 770, 7802 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.