Highest Common Factor of 6770, 1770, 18998 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 6770, 1770, 18998 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6770, 1770, 18998 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 6770, 1770, 18998 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 6770, 1770, 18998 is 2.
HCF(6770, 1770, 18998) = 2
HCF of 6770, 1770, 18998 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6770, 1770, 18998 is 2.
Highest Common Factor of 6770,1770,18998 is 2
Step 1: Since 6770 > 1770, we apply the division lemma to 6770 and 1770, to get
6770 = 1770 x 3 + 1460
Step 2: Since the reminder 1770 ≠ 0, we apply division lemma to 1460 and 1770, to get
1770 = 1460 x 1 + 310
Step 3: We consider the new divisor 1460 and the new remainder 310, and apply the division lemma to get
1460 = 310 x 4 + 220
We consider the new divisor 310 and the new remainder 220,and apply the division lemma to get
310 = 220 x 1 + 90
We consider the new divisor 220 and the new remainder 90,and apply the division lemma to get
220 = 90 x 2 + 40
We consider the new divisor 90 and the new remainder 40,and apply the division lemma to get
90 = 40 x 2 + 10
We consider the new divisor 40 and the new remainder 10,and apply the division lemma to get
40 = 10 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 6770 and 1770 is 10
Notice that 10 = HCF(40,10) = HCF(90,40) = HCF(220,90) = HCF(310,220) = HCF(1460,310) = HCF(1770,1460) = HCF(6770,1770) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 18998 > 10, we apply the division lemma to 18998 and 10, to get
18998 = 10 x 1899 + 8
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 8 and 10, to get
10 = 8 x 1 + 2
Step 3: 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 10 and 18998 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(18998,10) .
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Frequently Asked Questions on HCF of 6770, 1770, 18998 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 6770, 1770, 18998?
Answer: HCF of 6770, 1770, 18998 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6770, 1770, 18998 using Euclid's Algorithm?
Answer: For arbitrary numbers 6770, 1770, 18998 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.