Highest Common Factor of 435, 660, 14 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 435, 660, 14 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 435, 660, 14 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 435, 660, 14 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 435, 660, 14 is 1.
HCF(435, 660, 14) = 1
HCF of 435, 660, 14 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 435, 660, 14 is 1.
Highest Common Factor of 435,660,14 is 1
Step 1: Since 660 > 435, we apply the division lemma to 660 and 435, to get
660 = 435 x 1 + 225
Step 2: Since the reminder 435 ≠ 0, we apply division lemma to 225 and 435, to get
435 = 225 x 1 + 210
Step 3: We consider the new divisor 225 and the new remainder 210, and apply the division lemma to get
225 = 210 x 1 + 15
We consider the new divisor 210 and the new remainder 15, and apply the division lemma to get
210 = 15 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 435 and 660 is 15
Notice that 15 = HCF(210,15) = HCF(225,210) = HCF(435,225) = HCF(660,435) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 15 > 14, we apply the division lemma to 15 and 14, to get
15 = 14 x 1 + 1
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 1 and 14, to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 15 and 14 is 1
Notice that 1 = HCF(14,1) = HCF(15,14) .
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Frequently Asked Questions on HCF of 435, 660, 14 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 435, 660, 14?
Answer: HCF of 435, 660, 14 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 435, 660, 14 using Euclid's Algorithm?
Answer: For arbitrary numbers 435, 660, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.