Highest Common Factor of 866, 456, 474 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 866, 456, 474 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 866, 456, 474 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 866, 456, 474 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 866, 456, 474 is 2.
HCF(866, 456, 474) = 2
HCF of 866, 456, 474 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 866, 456, 474 is 2.
Highest Common Factor of 866,456,474 is 2
Step 1: Since 866 > 456, we apply the division lemma to 866 and 456, to get
866 = 456 x 1 + 410
Step 2: Since the reminder 456 ≠ 0, we apply division lemma to 410 and 456, to get
456 = 410 x 1 + 46
Step 3: We consider the new divisor 410 and the new remainder 46, and apply the division lemma to get
410 = 46 x 8 + 42
We consider the new divisor 46 and the new remainder 42,and apply the division lemma to get
46 = 42 x 1 + 4
We consider the new divisor 42 and the new remainder 4,and apply the division lemma to get
42 = 4 x 10 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 866 and 456 is 2
Notice that 2 = HCF(4,2) = HCF(42,4) = HCF(46,42) = HCF(410,46) = HCF(456,410) = HCF(866,456) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 474 > 2, we apply the division lemma to 474 and 2, to get
474 = 2 x 237 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 474 is 2
Notice that 2 = HCF(474,2) .
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Frequently Asked Questions on HCF of 866, 456, 474 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 866, 456, 474?
Answer: HCF of 866, 456, 474 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 866, 456, 474 using Euclid's Algorithm?
Answer: For arbitrary numbers 866, 456, 474 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.