Highest Common Factor of 306, 802, 698 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 306, 802, 698 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 306, 802, 698 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 306, 802, 698 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 306, 802, 698 is 2.
HCF(306, 802, 698) = 2
HCF of 306, 802, 698 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 306, 802, 698 is 2.
Highest Common Factor of 306,802,698 is 2
Step 1: Since 802 > 306, we apply the division lemma to 802 and 306, to get
802 = 306 x 2 + 190
Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 190 and 306, to get
306 = 190 x 1 + 116
Step 3: We consider the new divisor 190 and the new remainder 116, and apply the division lemma to get
190 = 116 x 1 + 74
We consider the new divisor 116 and the new remainder 74,and apply the division lemma to get
116 = 74 x 1 + 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 306 and 802 is 2
Notice that 2 = HCF(10,2) = HCF(32,10) = HCF(42,32) = HCF(74,42) = HCF(116,74) = HCF(190,116) = HCF(306,190) = HCF(802,306) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 698 > 2, we apply the division lemma to 698 and 2, to get
698 = 2 x 349 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 698 is 2
Notice that 2 = HCF(698,2) .
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Frequently Asked Questions on HCF of 306, 802, 698 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 306, 802, 698?
Answer: HCF of 306, 802, 698 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 306, 802, 698 using Euclid's Algorithm?
Answer: For arbitrary numbers 306, 802, 698 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.