Highest Common Factor of 704, 968, 127 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, 968, 127 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 704, 968, 127 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, 968, 127 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, 968, 127 is 1.
HCF(704, 968, 127) = 1
HCF of 704, 968, 127 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, 968, 127 is 1.
Highest Common Factor of 704,968,127 is 1
Step 1: Since 968 > 704, we apply the division lemma to 968 and 704, to get
968 = 704 x 1 + 264
Step 2: Since the reminder 704 ≠ 0, we apply division lemma to 264 and 704, to get
704 = 264 x 2 + 176
Step 3: We consider the new divisor 264 and the new remainder 176, and apply the division lemma to get
264 = 176 x 1 + 88
We consider the new divisor 176 and the new remainder 88, and apply the division lemma to get
176 = 88 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 88, the HCF of 704 and 968 is 88
Notice that 88 = HCF(176,88) = HCF(264,176) = HCF(704,264) = HCF(968,704) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 127 > 88, we apply the division lemma to 127 and 88, to get
127 = 88 x 1 + 39
Step 2: Since the reminder 88 ≠ 0, we apply division lemma to 39 and 88, to get
88 = 39 x 2 + 10
Step 3: We consider the new divisor 39 and the new remainder 10, and apply the division lemma to get
39 = 10 x 3 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 88 and 127 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(39,10) = HCF(88,39) = HCF(127,88) .
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Frequently Asked Questions on HCF of 704, 968, 127 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, 968, 127?
Answer: HCF of 704, 968, 127 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 704, 968, 127 using Euclid's Algorithm?
Answer: For arbitrary numbers 704, 968, 127 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.