Highest Common Factor of 340, 7785 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 340, 7785 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 340, 7785 is 5 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 340, 7785 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 340, 7785 is 5.
HCF(340, 7785) = 5
HCF of 340, 7785 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 340, 7785 is 5.
Highest Common Factor of 340,7785 is 5
Step 1: Since 7785 > 340, we apply the division lemma to 7785 and 340, to get
7785 = 340 x 22 + 305
Step 2: Since the reminder 340 ≠ 0, we apply division lemma to 305 and 340, to get
340 = 305 x 1 + 35
Step 3: We consider the new divisor 305 and the new remainder 35, and apply the division lemma to get
305 = 35 x 8 + 25
We consider the new divisor 35 and the new remainder 25,and apply the division lemma to get
35 = 25 x 1 + 10
We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get
25 = 10 x 2 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 340 and 7785 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) = HCF(305,35) = HCF(340,305) = HCF(7785,340) .
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Frequently Asked Questions on HCF of 340, 7785 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 340, 7785?
Answer: HCF of 340, 7785 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 340, 7785 using Euclid's Algorithm?
Answer: For arbitrary numbers 340, 7785 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.