Highest Common Factor of 705, 972, 421 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 705, 972, 421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 972, 421 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 705, 972, 421 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 705, 972, 421 is 1.
HCF(705, 972, 421) = 1
HCF of 705, 972, 421 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 705, 972, 421 is 1.
Highest Common Factor of 705,972,421 is 1
Step 1: Since 972 > 705, we apply the division lemma to 972 and 705, to get
972 = 705 x 1 + 267
Step 2: Since the reminder 705 ≠ 0, we apply division lemma to 267 and 705, to get
705 = 267 x 2 + 171
Step 3: We consider the new divisor 267 and the new remainder 171, and apply the division lemma to get
267 = 171 x 1 + 96
We consider the new divisor 171 and the new remainder 96,and apply the division lemma to get
171 = 96 x 1 + 75
We consider the new divisor 96 and the new remainder 75,and apply the division lemma to get
96 = 75 x 1 + 21
We consider the new divisor 75 and the new remainder 21,and apply the division lemma to get
75 = 21 x 3 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 705 and 972 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(75,21) = HCF(96,75) = HCF(171,96) = HCF(267,171) = HCF(705,267) = HCF(972,705) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 421 > 3, we apply the division lemma to 421 and 3, to get
421 = 3 x 140 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 421 is 1
Notice that 1 = HCF(3,1) = HCF(421,3) .
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Frequently Asked Questions on HCF of 705, 972, 421 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 705, 972, 421?
Answer: HCF of 705, 972, 421 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 972, 421 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 972, 421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.