Highest Common Factor of 408, 360, 851 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 408, 360, 851 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 408, 360, 851 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 408, 360, 851 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 408, 360, 851 is 1.
HCF(408, 360, 851) = 1
HCF of 408, 360, 851 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 408, 360, 851 is 1.
Highest Common Factor of 408,360,851 is 1
Step 1: Since 408 > 360, we apply the division lemma to 408 and 360, to get
408 = 360 x 1 + 48
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 48 and 360, to get
360 = 48 x 7 + 24
Step 3: We consider the new divisor 48 and the new remainder 24, and apply the division lemma to get
48 = 24 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 408 and 360 is 24
Notice that 24 = HCF(48,24) = HCF(360,48) = HCF(408,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 851 > 24, we apply the division lemma to 851 and 24, to get
851 = 24 x 35 + 11
Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 11 and 24, to get
24 = 11 x 2 + 2
Step 3: We consider the new divisor 11 and the new remainder 2, and apply the division lemma to get
11 = 2 x 5 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 24 and 851 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(24,11) = HCF(851,24) .
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Frequently Asked Questions on HCF of 408, 360, 851 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 408, 360, 851?
Answer: HCF of 408, 360, 851 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 408, 360, 851 using Euclid's Algorithm?
Answer: For arbitrary numbers 408, 360, 851 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.