Highest Common Factor of 785, 670 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 785, 670 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 785, 670 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 785, 670 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 785, 670 is 5.
HCF(785, 670) = 5
HCF of 785, 670 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 785, 670 is 5.
Highest Common Factor of 785,670 is 5
Step 1: Since 785 > 670, we apply the division lemma to 785 and 670, to get
785 = 670 x 1 + 115
Step 2: Since the reminder 670 ≠ 0, we apply division lemma to 115 and 670, to get
670 = 115 x 5 + 95
Step 3: We consider the new divisor 115 and the new remainder 95, and apply the division lemma to get
115 = 95 x 1 + 20
We consider the new divisor 95 and the new remainder 20,and apply the division lemma to get
95 = 20 x 4 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 785 and 670 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(95,20) = HCF(115,95) = HCF(670,115) = HCF(785,670) .
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Frequently Asked Questions on HCF of 785, 670 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 785, 670?
Answer: HCF of 785, 670 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 785, 670 using Euclid's Algorithm?
Answer: For arbitrary numbers 785, 670 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
