Highest Common Factor of 902, 658, 418 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 902, 658, 418 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 902, 658, 418 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 902, 658, 418 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 902, 658, 418 is 2.
HCF(902, 658, 418) = 2
HCF of 902, 658, 418 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 902, 658, 418 is 2.
Highest Common Factor of 902,658,418 is 2
Step 1: Since 902 > 658, we apply the division lemma to 902 and 658, to get
902 = 658 x 1 + 244
Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 244 and 658, to get
658 = 244 x 2 + 170
Step 3: We consider the new divisor 244 and the new remainder 170, and apply the division lemma to get
244 = 170 x 1 + 74
We consider the new divisor 170 and the new remainder 74,and apply the division lemma to get
170 = 74 x 2 + 22
We consider the new divisor 74 and the new remainder 22,and apply the division lemma to get
74 = 22 x 3 + 8
We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get
22 = 8 x 2 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 902 and 658 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(74,22) = HCF(170,74) = HCF(244,170) = HCF(658,244) = HCF(902,658) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 418 > 2, we apply the division lemma to 418 and 2, to get
418 = 2 x 209 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 418 is 2
Notice that 2 = HCF(418,2) .
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Frequently Asked Questions on HCF of 902, 658, 418 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 902, 658, 418?
Answer: HCF of 902, 658, 418 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 902, 658, 418 using Euclid's Algorithm?
Answer: For arbitrary numbers 902, 658, 418 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.