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 789, 492, 419 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 789, 492, 419 is 1 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 789, 492, 419 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 789, 492, 419 is 1.
HCF(789, 492, 419) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 789, 492, 419 is 1.
Step 1: Since 789 > 492, we apply the division lemma to 789 and 492, to get
789 = 492 x 1 + 297
Step 2: Since the reminder 492 ≠ 0, we apply division lemma to 297 and 492, to get
492 = 297 x 1 + 195
Step 3: We consider the new divisor 297 and the new remainder 195, and apply the division lemma to get
297 = 195 x 1 + 102
We consider the new divisor 195 and the new remainder 102,and apply the division lemma to get
195 = 102 x 1 + 93
We consider the new divisor 102 and the new remainder 93,and apply the division lemma to get
102 = 93 x 1 + 9
We consider the new divisor 93 and the new remainder 9,and apply the division lemma to get
93 = 9 x 10 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 789 and 492 is 3
Notice that 3 = HCF(9,3) = HCF(93,9) = HCF(102,93) = HCF(195,102) = HCF(297,195) = HCF(492,297) = HCF(789,492) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 419 > 3, we apply the division lemma to 419 and 3, to get
419 = 3 x 139 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 419 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(419,3) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 789, 492, 419?
Answer: HCF of 789, 492, 419 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 789, 492, 419 using Euclid's Algorithm?
Answer: For arbitrary numbers 789, 492, 419 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.