Highest Common Factor of 420, 903, 659 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 420, 903, 659 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 903, 659 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 420, 903, 659 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 420, 903, 659 is 1.
HCF(420, 903, 659) = 1
HCF of 420, 903, 659 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 420, 903, 659 is 1.
Highest Common Factor of 420,903,659 is 1
Step 1: Since 903 > 420, we apply the division lemma to 903 and 420, to get
903 = 420 x 2 + 63
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 63 and 420, to get
420 = 63 x 6 + 42
Step 3: We consider the new divisor 63 and the new remainder 42, and apply the division lemma to get
63 = 42 x 1 + 21
We consider the new divisor 42 and the new remainder 21, and apply the division lemma to get
42 = 21 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 420 and 903 is 21
Notice that 21 = HCF(42,21) = HCF(63,42) = HCF(420,63) = HCF(903,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 659 > 21, we apply the division lemma to 659 and 21, to get
659 = 21 x 31 + 8
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 8 and 21, to get
21 = 8 x 2 + 5
Step 3: We consider the new divisor 8 and the new remainder 5, and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 21 and 659 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(659,21) .
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Frequently Asked Questions on HCF of 420, 903, 659 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 420, 903, 659?
Answer: HCF of 420, 903, 659 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 903, 659 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 903, 659 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.