Highest Common Factor of 336, 861, 451 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 336, 861, 451 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 336, 861, 451 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 336, 861, 451 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 336, 861, 451 is 1.
HCF(336, 861, 451) = 1
HCF of 336, 861, 451 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 336, 861, 451 is 1.
Highest Common Factor of 336,861,451 is 1
Step 1: Since 861 > 336, we apply the division lemma to 861 and 336, to get
861 = 336 x 2 + 189
Step 2: Since the reminder 336 ≠ 0, we apply division lemma to 189 and 336, to get
336 = 189 x 1 + 147
Step 3: We consider the new divisor 189 and the new remainder 147, and apply the division lemma to get
189 = 147 x 1 + 42
We consider the new divisor 147 and the new remainder 42,and apply the division lemma to get
147 = 42 x 3 + 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 336 and 861 is 21
Notice that 21 = HCF(42,21) = HCF(147,42) = HCF(189,147) = HCF(336,189) = HCF(861,336) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 451 > 21, we apply the division lemma to 451 and 21, to get
451 = 21 x 21 + 10
Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 10 and 21, to get
21 = 10 x 2 + 1
Step 3: We consider the new divisor 10 and the new remainder 1, and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 21 and 451 is 1
Notice that 1 = HCF(10,1) = HCF(21,10) = HCF(451,21) .
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Frequently Asked Questions on HCF of 336, 861, 451 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 336, 861, 451?
Answer: HCF of 336, 861, 451 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 336, 861, 451 using Euclid's Algorithm?
Answer: For arbitrary numbers 336, 861, 451 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.