Highest Common Factor of 578, 680, 985 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 578, 680, 985 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 578, 680, 985 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 578, 680, 985 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 578, 680, 985 is 1.
HCF(578, 680, 985) = 1
HCF of 578, 680, 985 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 578, 680, 985 is 1.
Highest Common Factor of 578,680,985 is 1
Step 1: Since 680 > 578, we apply the division lemma to 680 and 578, to get
680 = 578 x 1 + 102
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 102 and 578, to get
578 = 102 x 5 + 68
Step 3: We consider the new divisor 102 and the new remainder 68, and apply the division lemma to get
102 = 68 x 1 + 34
We consider the new divisor 68 and the new remainder 34, and apply the division lemma to get
68 = 34 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 34, the HCF of 578 and 680 is 34
Notice that 34 = HCF(68,34) = HCF(102,68) = HCF(578,102) = HCF(680,578) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 985 > 34, we apply the division lemma to 985 and 34, to get
985 = 34 x 28 + 33
Step 2: Since the reminder 34 ≠ 0, we apply division lemma to 33 and 34, to get
34 = 33 x 1 + 1
Step 3: We consider the new divisor 33 and the new remainder 1, and apply the division lemma to get
33 = 1 x 33 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 34 and 985 is 1
Notice that 1 = HCF(33,1) = HCF(34,33) = HCF(985,34) .
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Frequently Asked Questions on HCF of 578, 680, 985 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 578, 680, 985?
Answer: HCF of 578, 680, 985 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 578, 680, 985 using Euclid's Algorithm?
Answer: For arbitrary numbers 578, 680, 985 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.