Highest Common Factor of 1672, 7705 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 1672, 7705 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 1672, 7705 is 1 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 1672, 7705 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 1672, 7705 is 1.
HCF(1672, 7705) = 1
HCF of 1672, 7705 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1672, 7705 is 1.
Highest Common Factor of 1672,7705 is 1
Step 1: Since 7705 > 1672, we apply the division lemma to 7705 and 1672, to get
7705 = 1672 x 4 + 1017
Step 2: Since the reminder 1672 ≠ 0, we apply division lemma to 1017 and 1672, to get
1672 = 1017 x 1 + 655
Step 3: We consider the new divisor 1017 and the new remainder 655, and apply the division lemma to get
1017 = 655 x 1 + 362
We consider the new divisor 655 and the new remainder 362,and apply the division lemma to get
655 = 362 x 1 + 293
We consider the new divisor 362 and the new remainder 293,and apply the division lemma to get
362 = 293 x 1 + 69
We consider the new divisor 293 and the new remainder 69,and apply the division lemma to get
293 = 69 x 4 + 17
We consider the new divisor 69 and the new remainder 17,and apply the division lemma to get
69 = 17 x 4 + 1
We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1672 and 7705 is 1
Notice that 1 = HCF(17,1) = HCF(69,17) = HCF(293,69) = HCF(362,293) = HCF(655,362) = HCF(1017,655) = HCF(1672,1017) = HCF(7705,1672) .
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Frequently Asked Questions on HCF of 1672, 7705 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 1672, 7705?
Answer: HCF of 1672, 7705 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1672, 7705 using Euclid's Algorithm?
Answer: For arbitrary numbers 1672, 7705 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
