Highest Common Factor of 714, 578, 976 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 714, 578, 976 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 714, 578, 976 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 714, 578, 976 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 714, 578, 976 is 2.
HCF(714, 578, 976) = 2
HCF of 714, 578, 976 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 714, 578, 976 is 2.
Highest Common Factor of 714,578,976 is 2
Step 1: Since 714 > 578, we apply the division lemma to 714 and 578, to get
714 = 578 x 1 + 136
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 136 and 578, to get
578 = 136 x 4 + 34
Step 3: We consider the new divisor 136 and the new remainder 34, and apply the division lemma to get
136 = 34 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 714 and 578 is 34
Notice that 34 = HCF(136,34) = HCF(578,136) = HCF(714,578) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 976 > 34, we apply the division lemma to 976 and 34, to get
976 = 34 x 28 + 24
Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 24 and 34, to get
34 = 24 x 1 + 10
Step 3: We consider the new divisor 24 and the new remainder 10, and apply the division lemma to get
24 = 10 x 2 + 4
We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get
10 = 4 x 2 + 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 34 and 976 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(24,10) = HCF(34,24) = HCF(976,34) .
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Frequently Asked Questions on HCF of 714, 578, 976 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 714, 578, 976?
Answer: HCF of 714, 578, 976 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 714, 578, 976 using Euclid's Algorithm?
Answer: For arbitrary numbers 714, 578, 976 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.