Highest Common Factor of 472, 860, 104 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 472, 860, 104 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 472, 860, 104 is 4 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 472, 860, 104 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 472, 860, 104 is 4.
HCF(472, 860, 104) = 4
HCF of 472, 860, 104 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 472, 860, 104 is 4.
Highest Common Factor of 472,860,104 is 4
Step 1: Since 860 > 472, we apply the division lemma to 860 and 472, to get
860 = 472 x 1 + 388
Step 2: Since the reminder 472 ≠ 0, we apply division lemma to 388 and 472, to get
472 = 388 x 1 + 84
Step 3: We consider the new divisor 388 and the new remainder 84, and apply the division lemma to get
388 = 84 x 4 + 52
We consider the new divisor 84 and the new remainder 52,and apply the division lemma to get
84 = 52 x 1 + 32
We consider the new divisor 52 and the new remainder 32,and apply the division lemma to get
52 = 32 x 1 + 20
We consider the new divisor 32 and the new remainder 20,and apply the division lemma to get
32 = 20 x 1 + 12
We consider the new divisor 20 and the new remainder 12,and apply the division lemma to get
20 = 12 x 1 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 472 and 860 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(20,12) = HCF(32,20) = HCF(52,32) = HCF(84,52) = HCF(388,84) = HCF(472,388) = HCF(860,472) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 104 > 4, we apply the division lemma to 104 and 4, to get
104 = 4 x 26 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 104 is 4
Notice that 4 = HCF(104,4) .
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Frequently Asked Questions on HCF of 472, 860, 104 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 472, 860, 104?
Answer: HCF of 472, 860, 104 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 472, 860, 104 using Euclid's Algorithm?
Answer: For arbitrary numbers 472, 860, 104 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.