Highest Common Factor of 698, 1300, 3070 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 698, 1300, 3070 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 698, 1300, 3070 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 698, 1300, 3070 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 698, 1300, 3070 is 2.
HCF(698, 1300, 3070) = 2
HCF of 698, 1300, 3070 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 698, 1300, 3070 is 2.
Highest Common Factor of 698,1300,3070 is 2
Step 1: Since 1300 > 698, we apply the division lemma to 1300 and 698, to get
1300 = 698 x 1 + 602
Step 2: Since the reminder 698 ≠ 0, we apply division lemma to 602 and 698, to get
698 = 602 x 1 + 96
Step 3: We consider the new divisor 602 and the new remainder 96, and apply the division lemma to get
602 = 96 x 6 + 26
We consider the new divisor 96 and the new remainder 26,and apply the division lemma to get
96 = 26 x 3 + 18
We consider the new divisor 26 and the new remainder 18,and apply the division lemma to get
26 = 18 x 1 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 698 and 1300 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(26,18) = HCF(96,26) = HCF(602,96) = HCF(698,602) = HCF(1300,698) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3070 > 2, we apply the division lemma to 3070 and 2, to get
3070 = 2 x 1535 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 3070 is 2
Notice that 2 = HCF(3070,2) .
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Frequently Asked Questions on HCF of 698, 1300, 3070 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 698, 1300, 3070?
Answer: HCF of 698, 1300, 3070 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 698, 1300, 3070 using Euclid's Algorithm?
Answer: For arbitrary numbers 698, 1300, 3070 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.