Highest Common Factor of 630, 980, 654 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 630, 980, 654 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 630, 980, 654 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 630, 980, 654 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 630, 980, 654 is 2.
HCF(630, 980, 654) = 2
HCF of 630, 980, 654 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 630, 980, 654 is 2.
Highest Common Factor of 630,980,654 is 2
Step 1: Since 980 > 630, we apply the division lemma to 980 and 630, to get
980 = 630 x 1 + 350
Step 2: Since the reminder 630 ≠ 0, we apply division lemma to 350 and 630, to get
630 = 350 x 1 + 280
Step 3: We consider the new divisor 350 and the new remainder 280, and apply the division lemma to get
350 = 280 x 1 + 70
We consider the new divisor 280 and the new remainder 70, and apply the division lemma to get
280 = 70 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 70, the HCF of 630 and 980 is 70
Notice that 70 = HCF(280,70) = HCF(350,280) = HCF(630,350) = HCF(980,630) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 654 > 70, we apply the division lemma to 654 and 70, to get
654 = 70 x 9 + 24
Step 2: Since the reminder 70 ≠ 0, we apply division lemma to 24 and 70, to get
70 = 24 x 2 + 22
Step 3: We consider the new divisor 24 and the new remainder 22, and apply the division lemma to get
24 = 22 x 1 + 2
We consider the new divisor 22 and the new remainder 2, and apply the division lemma to get
22 = 2 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 70 and 654 is 2
Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(70,24) = HCF(654,70) .
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Frequently Asked Questions on HCF of 630, 980, 654 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 630, 980, 654?
Answer: HCF of 630, 980, 654 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 630, 980, 654 using Euclid's Algorithm?
Answer: For arbitrary numbers 630, 980, 654 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.