Highest Common Factor of 644, 454, 980 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 644, 454, 980 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 644, 454, 980 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 644, 454, 980 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 644, 454, 980 is 2.
HCF(644, 454, 980) = 2
HCF of 644, 454, 980 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 644, 454, 980 is 2.
Highest Common Factor of 644,454,980 is 2
Step 1: Since 644 > 454, we apply the division lemma to 644 and 454, to get
644 = 454 x 1 + 190
Step 2: Since the reminder 454 ≠ 0, we apply division lemma to 190 and 454, to get
454 = 190 x 2 + 74
Step 3: We consider the new divisor 190 and the new remainder 74, and apply the division lemma to get
190 = 74 x 2 + 42
We consider the new divisor 74 and the new remainder 42,and apply the division lemma to get
74 = 42 x 1 + 32
We consider the new divisor 42 and the new remainder 32,and apply the division lemma to get
42 = 32 x 1 + 10
We consider the new divisor 32 and the new remainder 10,and apply the division lemma to get
32 = 10 x 3 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 644 and 454 is 2
Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(42,32) = HCF(74,42) = HCF(190,74) = HCF(454,190) = HCF(644,454) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 980 > 2, we apply the division lemma to 980 and 2, to get
980 = 2 x 490 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 980 is 2
Notice that 2 = HCF(980,2) .
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Frequently Asked Questions on HCF of 644, 454, 980 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 644, 454, 980?
Answer: HCF of 644, 454, 980 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 644, 454, 980 using Euclid's Algorithm?
Answer: For arbitrary numbers 644, 454, 980 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.