Highest Common Factor of 420, 656, 10 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, 656, 10 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 656, 10 is 2 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, 656, 10 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, 656, 10 is 2.
HCF(420, 656, 10) = 2
HCF of 420, 656, 10 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, 656, 10 is 2.
Highest Common Factor of 420,656,10 is 2
Step 1: Since 656 > 420, we apply the division lemma to 656 and 420, to get
656 = 420 x 1 + 236
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 236 and 420, to get
420 = 236 x 1 + 184
Step 3: We consider the new divisor 236 and the new remainder 184, and apply the division lemma to get
236 = 184 x 1 + 52
We consider the new divisor 184 and the new remainder 52,and apply the division lemma to get
184 = 52 x 3 + 28
We consider the new divisor 52 and the new remainder 28,and apply the division lemma to get
52 = 28 x 1 + 24
We consider the new divisor 28 and the new remainder 24,and apply the division lemma to get
28 = 24 x 1 + 4
We consider the new divisor 24 and the new remainder 4,and apply the division lemma to get
24 = 4 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 420 and 656 is 4
Notice that 4 = HCF(24,4) = HCF(28,24) = HCF(52,28) = HCF(184,52) = HCF(236,184) = HCF(420,236) = HCF(656,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 10 > 4, we apply the division lemma to 10 and 4, to get
10 = 4 x 2 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 10 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) .
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Frequently Asked Questions on HCF of 420, 656, 10 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, 656, 10?
Answer: HCF of 420, 656, 10 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 656, 10 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 656, 10 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.