Highest Common Factor of 704, 1205 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 704, 1205 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 704, 1205 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 704, 1205 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 704, 1205 is 1.
HCF(704, 1205) = 1
HCF of 704, 1205 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 704, 1205 is 1.
Highest Common Factor of 704,1205 is 1
Step 1: Since 1205 > 704, we apply the division lemma to 1205 and 704, to get
1205 = 704 x 1 + 501
Step 2: Since the reminder 704 ≠ 0, we apply division lemma to 501 and 704, to get
704 = 501 x 1 + 203
Step 3: We consider the new divisor 501 and the new remainder 203, and apply the division lemma to get
501 = 203 x 2 + 95
We consider the new divisor 203 and the new remainder 95,and apply the division lemma to get
203 = 95 x 2 + 13
We consider the new divisor 95 and the new remainder 13,and apply the division lemma to get
95 = 13 x 7 + 4
We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 704 and 1205 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(95,13) = HCF(203,95) = HCF(501,203) = HCF(704,501) = HCF(1205,704) .
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Frequently Asked Questions on HCF of 704, 1205 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 704, 1205?
Answer: HCF of 704, 1205 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 704, 1205 using Euclid's Algorithm?
Answer: For arbitrary numbers 704, 1205 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.