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 608, 912, 529 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 608, 912, 529 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 608, 912, 529 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 608, 912, 529 is 1.
HCF(608, 912, 529) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 608, 912, 529 is 1.
Step 1: Since 912 > 608, we apply the division lemma to 912 and 608, to get
912 = 608 x 1 + 304
Step 2: Since the reminder 608 ≠ 0, we apply division lemma to 304 and 608, to get
608 = 304 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 304, the HCF of 608 and 912 is 304
Notice that 304 = HCF(608,304) = HCF(912,608) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 529 > 304, we apply the division lemma to 529 and 304, to get
529 = 304 x 1 + 225
Step 2: Since the reminder 304 ≠ 0, we apply division lemma to 225 and 304, to get
304 = 225 x 1 + 79
Step 3: We consider the new divisor 225 and the new remainder 79, and apply the division lemma to get
225 = 79 x 2 + 67
We consider the new divisor 79 and the new remainder 67,and apply the division lemma to get
79 = 67 x 1 + 12
We consider the new divisor 67 and the new remainder 12,and apply the division lemma to get
67 = 12 x 5 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
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 304 and 529 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(67,12) = HCF(79,67) = HCF(225,79) = HCF(304,225) = HCF(529,304) .
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 608, 912, 529?
Answer: HCF of 608, 912, 529 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 608, 912, 529 using Euclid's Algorithm?
Answer: For arbitrary numbers 608, 912, 529 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.