Highest Common Factor of 705, 435, 414 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, 435, 414 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 705, 435, 414 is 3 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, 435, 414 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, 435, 414 is 3.
HCF(705, 435, 414) = 3
HCF of 705, 435, 414 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, 435, 414 is 3.
Highest Common Factor of 705,435,414 is 3
Step 1: Since 705 > 435, we apply the division lemma to 705 and 435, to get
705 = 435 x 1 + 270
Step 2: Since the reminder 435 ≠ 0, we apply division lemma to 270 and 435, to get
435 = 270 x 1 + 165
Step 3: We consider the new divisor 270 and the new remainder 165, and apply the division lemma to get
270 = 165 x 1 + 105
We consider the new divisor 165 and the new remainder 105,and apply the division lemma to get
165 = 105 x 1 + 60
We consider the new divisor 105 and the new remainder 60,and apply the division lemma to get
105 = 60 x 1 + 45
We consider the new divisor 60 and the new remainder 45,and apply the division lemma to get
60 = 45 x 1 + 15
We consider the new divisor 45 and the new remainder 15,and apply the division lemma to get
45 = 15 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 705 and 435 is 15
Notice that 15 = HCF(45,15) = HCF(60,45) = HCF(105,60) = HCF(165,105) = HCF(270,165) = HCF(435,270) = HCF(705,435) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 414 > 15, we apply the division lemma to 414 and 15, to get
414 = 15 x 27 + 9
Step 2: Since the reminder 15 ≠ 0, we apply division lemma to 9 and 15, to get
15 = 9 x 1 + 6
Step 3: We consider the new divisor 9 and the new remainder 6, and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3, and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 15 and 414 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(414,15) .
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Frequently Asked Questions on HCF of 705, 435, 414 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, 435, 414?
Answer: HCF of 705, 435, 414 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 705, 435, 414 using Euclid's Algorithm?
Answer: For arbitrary numbers 705, 435, 414 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.