Highest Common Factor of 407, 968, 854 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 407, 968, 854 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 407, 968, 854 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 407, 968, 854 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 407, 968, 854 is 1.
HCF(407, 968, 854) = 1
HCF of 407, 968, 854 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 407, 968, 854 is 1.
Highest Common Factor of 407,968,854 is 1
Step 1: Since 968 > 407, we apply the division lemma to 968 and 407, to get
968 = 407 x 2 + 154
Step 2: Since the reminder 407 ≠ 0, we apply division lemma to 154 and 407, to get
407 = 154 x 2 + 99
Step 3: We consider the new divisor 154 and the new remainder 99, and apply the division lemma to get
154 = 99 x 1 + 55
We consider the new divisor 99 and the new remainder 55,and apply the division lemma to get
99 = 55 x 1 + 44
We consider the new divisor 55 and the new remainder 44,and apply the division lemma to get
55 = 44 x 1 + 11
We consider the new divisor 44 and the new remainder 11,and apply the division lemma to get
44 = 11 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 11, the HCF of 407 and 968 is 11
Notice that 11 = HCF(44,11) = HCF(55,44) = HCF(99,55) = HCF(154,99) = HCF(407,154) = HCF(968,407) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 854 > 11, we apply the division lemma to 854 and 11, to get
854 = 11 x 77 + 7
Step 2: Since the reminder 11 ≠ 0, we apply division lemma to 7 and 11, to get
11 = 7 x 1 + 4
Step 3: We consider the new divisor 7 and the new remainder 4, and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 11 and 854 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(854,11) .
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Frequently Asked Questions on HCF of 407, 968, 854 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 407, 968, 854?
Answer: HCF of 407, 968, 854 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 407, 968, 854 using Euclid's Algorithm?
Answer: For arbitrary numbers 407, 968, 854 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.