Highest Common Factor of 510, 694, 120, 98 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 510, 694, 120, 98 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 510, 694, 120, 98 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 510, 694, 120, 98 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 510, 694, 120, 98 is 2.
HCF(510, 694, 120, 98) = 2
HCF of 510, 694, 120, 98 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 510, 694, 120, 98 is 2.
Highest Common Factor of 510,694,120,98 is 2
Step 1: Since 694 > 510, we apply the division lemma to 694 and 510, to get
694 = 510 x 1 + 184
Step 2: Since the reminder 510 ≠ 0, we apply division lemma to 184 and 510, to get
510 = 184 x 2 + 142
Step 3: We consider the new divisor 184 and the new remainder 142, and apply the division lemma to get
184 = 142 x 1 + 42
We consider the new divisor 142 and the new remainder 42,and apply the division lemma to get
142 = 42 x 3 + 16
We consider the new divisor 42 and the new remainder 16,and apply the division lemma to get
42 = 16 x 2 + 10
We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 510 and 694 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(42,16) = HCF(142,42) = HCF(184,142) = HCF(510,184) = HCF(694,510) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 120 > 2, we apply the division lemma to 120 and 2, to get
120 = 2 x 60 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 120 is 2
Notice that 2 = HCF(120,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 98 > 2, we apply the division lemma to 98 and 2, to get
98 = 2 x 49 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 98 is 2
Notice that 2 = HCF(98,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 510, 694, 120, 98 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 510, 694, 120, 98?
Answer: HCF of 510, 694, 120, 98 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 510, 694, 120, 98 using Euclid's Algorithm?
Answer: For arbitrary numbers 510, 694, 120, 98 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.