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 658, 988, 724 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 658, 988, 724 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 658, 988, 724 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 658, 988, 724 is 2.
HCF(658, 988, 724) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 658, 988, 724 is 2.
Step 1: Since 988 > 658, we apply the division lemma to 988 and 658, to get
988 = 658 x 1 + 330
Step 2: Since the reminder 658 ≠ 0, we apply division lemma to 330 and 658, to get
658 = 330 x 1 + 328
Step 3: We consider the new divisor 330 and the new remainder 328, and apply the division lemma to get
330 = 328 x 1 + 2
We consider the new divisor 328 and the new remainder 2, and apply the division lemma to get
328 = 2 x 164 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 658 and 988 is 2
Notice that 2 = HCF(328,2) = HCF(330,328) = HCF(658,330) = HCF(988,658) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 724 > 2, we apply the division lemma to 724 and 2, to get
724 = 2 x 362 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 724 is 2
Notice that 2 = HCF(724,2) .
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 658, 988, 724?
Answer: HCF of 658, 988, 724 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 658, 988, 724 using Euclid's Algorithm?
Answer: For arbitrary numbers 658, 988, 724 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.