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 774, 602, 421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 774, 602, 421 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 774, 602, 421 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 774, 602, 421 is 1.
HCF(774, 602, 421) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 774, 602, 421 is 1.
Step 1: Since 774 > 602, we apply the division lemma to 774 and 602, to get
774 = 602 x 1 + 172
Step 2: Since the reminder 602 ≠ 0, we apply division lemma to 172 and 602, to get
602 = 172 x 3 + 86
Step 3: We consider the new divisor 172 and the new remainder 86, and apply the division lemma to get
172 = 86 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 86, the HCF of 774 and 602 is 86
Notice that 86 = HCF(172,86) = HCF(602,172) = HCF(774,602) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 421 > 86, we apply the division lemma to 421 and 86, to get
421 = 86 x 4 + 77
Step 2: Since the reminder 86 ≠ 0, we apply division lemma to 77 and 86, to get
86 = 77 x 1 + 9
Step 3: We consider the new divisor 77 and the new remainder 9, and apply the division lemma to get
77 = 9 x 8 + 5
We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get
9 = 5 x 1 + 4
We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get
5 = 4 x 1 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 86 and 421 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(77,9) = HCF(86,77) = HCF(421,86) .
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 774, 602, 421?
Answer: HCF of 774, 602, 421 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 774, 602, 421 using Euclid's Algorithm?
Answer: For arbitrary numbers 774, 602, 421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.