Highest Common Factor of 670, 105 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 670, 105 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 670, 105 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 670, 105 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 670, 105 is 5.
HCF(670, 105) = 5
HCF of 670, 105 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 670, 105 is 5.
Highest Common Factor of 670,105 is 5
Step 1: Since 670 > 105, we apply the division lemma to 670 and 105, to get
670 = 105 x 6 + 40
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 40 and 105, to get
105 = 40 x 2 + 25
Step 3: We consider the new divisor 40 and the new remainder 25, and apply the division lemma to get
40 = 25 x 1 + 15
We consider the new divisor 25 and the new remainder 15,and apply the division lemma to get
25 = 15 x 1 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 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 670 and 105 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(25,15) = HCF(40,25) = HCF(105,40) = HCF(670,105) .
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Frequently Asked Questions on HCF of 670, 105 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 670, 105?
Answer: HCF of 670, 105 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 670, 105 using Euclid's Algorithm?
Answer: For arbitrary numbers 670, 105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.