Highest Common Factor of 658, 898, 602 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 658, 898, 602 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 658, 898, 602 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 658, 898, 602 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 658, 898, 602 is 2.
HCF(658, 898, 602) = 2
HCF of 658, 898, 602 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 658, 898, 602 is 2.
Highest Common Factor of 658,898,602 is 2
Step 1: Since 898 > 658, we apply the division lemma to 898 and 658, to get
898 = 658 x 1 + 240
Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 240 and 658, to get
658 = 240 x 2 + 178
Step 3: We consider the new divisor 240 and the new remainder 178, and apply the division lemma to get
240 = 178 x 1 + 62
We consider the new divisor 178 and the new remainder 62,and apply the division lemma to get
178 = 62 x 2 + 54
We consider the new divisor 62 and the new remainder 54,and apply the division lemma to get
62 = 54 x 1 + 8
We consider the new divisor 54 and the new remainder 8,and apply the division lemma to get
54 = 8 x 6 + 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 658 and 898 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(54,8) = HCF(62,54) = HCF(178,62) = HCF(240,178) = HCF(658,240) = HCF(898,658) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 602 > 2, we apply the division lemma to 602 and 2, to get
602 = 2 x 301 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 602 is 2
Notice that 2 = HCF(602,2) .
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Frequently Asked Questions on HCF of 658, 898, 602 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 658, 898, 602?
Answer: HCF of 658, 898, 602 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 658, 898, 602 using Euclid's Algorithm?
Answer: For arbitrary numbers 658, 898, 602 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.