Highest Common Factor of 6945, 785 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 6945, 785 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 6945, 785 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 6945, 785 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 6945, 785 is 5.
HCF(6945, 785) = 5
HCF of 6945, 785 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6945, 785 is 5.
Highest Common Factor of 6945,785 is 5
Step 1: Since 6945 > 785, we apply the division lemma to 6945 and 785, to get
6945 = 785 x 8 + 665
Step 2: Since the reminder 785 ≠ 0, we apply division lemma to 665 and 785, to get
785 = 665 x 1 + 120
Step 3: We consider the new divisor 665 and the new remainder 120, and apply the division lemma to get
665 = 120 x 5 + 65
We consider the new divisor 120 and the new remainder 65,and apply the division lemma to get
120 = 65 x 1 + 55
We consider the new divisor 65 and the new remainder 55,and apply the division lemma to get
65 = 55 x 1 + 10
We consider the new divisor 55 and the new remainder 10,and apply the division lemma to get
55 = 10 x 5 + 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 6945 and 785 is 5
Notice that 5 = HCF(10,5) = HCF(55,10) = HCF(65,55) = HCF(120,65) = HCF(665,120) = HCF(785,665) = HCF(6945,785) .
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Frequently Asked Questions on HCF of 6945, 785 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 6945, 785?
Answer: HCF of 6945, 785 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6945, 785 using Euclid's Algorithm?
Answer: For arbitrary numbers 6945, 785 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.