Highest Common Factor of 928, 354, 646 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 928, 354, 646 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 928, 354, 646 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 928, 354, 646 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 928, 354, 646 is 2.
HCF(928, 354, 646) = 2
HCF of 928, 354, 646 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 928, 354, 646 is 2.
Highest Common Factor of 928,354,646 is 2
Step 1: Since 928 > 354, we apply the division lemma to 928 and 354, to get
928 = 354 x 2 + 220
Step 2: Since the reminder 354 ≠ 0, we apply division lemma to 220 and 354, to get
354 = 220 x 1 + 134
Step 3: We consider the new divisor 220 and the new remainder 134, and apply the division lemma to get
220 = 134 x 1 + 86
We consider the new divisor 134 and the new remainder 86,and apply the division lemma to get
134 = 86 x 1 + 48
We consider the new divisor 86 and the new remainder 48,and apply the division lemma to get
86 = 48 x 1 + 38
We consider the new divisor 48 and the new remainder 38,and apply the division lemma to get
48 = 38 x 1 + 10
We consider the new divisor 38 and the new remainder 10,and apply the division lemma to get
38 = 10 x 3 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 928 and 354 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(38,10) = HCF(48,38) = HCF(86,48) = HCF(134,86) = HCF(220,134) = HCF(354,220) = HCF(928,354) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 646 > 2, we apply the division lemma to 646 and 2, to get
646 = 2 x 323 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 646 is 2
Notice that 2 = HCF(646,2) .
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Frequently Asked Questions on HCF of 928, 354, 646 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 928, 354, 646?
Answer: HCF of 928, 354, 646 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 928, 354, 646 using Euclid's Algorithm?
Answer: For arbitrary numbers 928, 354, 646 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
