Highest Common Factor of 2154, 7098, 63720 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 2154, 7098, 63720 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 2154, 7098, 63720 is 6 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 2154, 7098, 63720 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 2154, 7098, 63720 is 6.
HCF(2154, 7098, 63720) = 6
HCF of 2154, 7098, 63720 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2154, 7098, 63720 is 6.
Highest Common Factor of 2154,7098,63720 is 6
Step 1: Since 7098 > 2154, we apply the division lemma to 7098 and 2154, to get
7098 = 2154 x 3 + 636
Step 2: Since the reminder 2154 ≠ 0, we apply division lemma to 636 and 2154, to get
2154 = 636 x 3 + 246
Step 3: We consider the new divisor 636 and the new remainder 246, and apply the division lemma to get
636 = 246 x 2 + 144
We consider the new divisor 246 and the new remainder 144,and apply the division lemma to get
246 = 144 x 1 + 102
We consider the new divisor 144 and the new remainder 102,and apply the division lemma to get
144 = 102 x 1 + 42
We consider the new divisor 102 and the new remainder 42,and apply the division lemma to get
102 = 42 x 2 + 18
We consider the new divisor 42 and the new remainder 18,and apply the division lemma to get
42 = 18 x 2 + 6
We consider the new divisor 18 and the new remainder 6,and apply the division lemma to get
18 = 6 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 2154 and 7098 is 6
Notice that 6 = HCF(18,6) = HCF(42,18) = HCF(102,42) = HCF(144,102) = HCF(246,144) = HCF(636,246) = HCF(2154,636) = HCF(7098,2154) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 63720 > 6, we apply the division lemma to 63720 and 6, to get
63720 = 6 x 10620 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6 and 63720 is 6
Notice that 6 = HCF(63720,6) .
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Frequently Asked Questions on HCF of 2154, 7098, 63720 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 2154, 7098, 63720?
Answer: HCF of 2154, 7098, 63720 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2154, 7098, 63720 using Euclid's Algorithm?
Answer: For arbitrary numbers 2154, 7098, 63720 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.