Highest Common Factor of 663, 870, 472 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 663, 870, 472 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 663, 870, 472 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 663, 870, 472 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 663, 870, 472 is 1.
HCF(663, 870, 472) = 1
HCF of 663, 870, 472 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 663, 870, 472 is 1.
Highest Common Factor of 663,870,472 is 1
Step 1: Since 870 > 663, we apply the division lemma to 870 and 663, to get
870 = 663 x 1 + 207
Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 207 and 663, to get
663 = 207 x 3 + 42
Step 3: We consider the new divisor 207 and the new remainder 42, and apply the division lemma to get
207 = 42 x 4 + 39
We consider the new divisor 42 and the new remainder 39,and apply the division lemma to get
42 = 39 x 1 + 3
We consider the new divisor 39 and the new remainder 3,and apply the division lemma to get
39 = 3 x 13 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 663 and 870 is 3
Notice that 3 = HCF(39,3) = HCF(42,39) = HCF(207,42) = HCF(663,207) = HCF(870,663) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 472 > 3, we apply the division lemma to 472 and 3, to get
472 = 3 x 157 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 472 is 1
Notice that 1 = HCF(3,1) = HCF(472,3) .
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Frequently Asked Questions on HCF of 663, 870, 472 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 663, 870, 472?
Answer: HCF of 663, 870, 472 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 663, 870, 472 using Euclid's Algorithm?
Answer: For arbitrary numbers 663, 870, 472 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.