Highest Common Factor of 359, 456, 724 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 359, 456, 724 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 359, 456, 724 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 359, 456, 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 359, 456, 724 is 1.
HCF(359, 456, 724) = 1
HCF of 359, 456, 724 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 359, 456, 724 is 1.
Highest Common Factor of 359,456,724 is 1
Step 1: Since 456 > 359, we apply the division lemma to 456 and 359, to get
456 = 359 x 1 + 97
Step 2: Since the reminder 359 ≠ 0, we apply division lemma to 97 and 359, to get
359 = 97 x 3 + 68
Step 3: We consider the new divisor 97 and the new remainder 68, and apply the division lemma to get
97 = 68 x 1 + 29
We consider the new divisor 68 and the new remainder 29,and apply the division lemma to get
68 = 29 x 2 + 10
We consider the new divisor 29 and the new remainder 10,and apply the division lemma to get
29 = 10 x 2 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 359 and 456 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(29,10) = HCF(68,29) = HCF(97,68) = HCF(359,97) = HCF(456,359) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 724 > 1, we apply the division lemma to 724 and 1, to get
724 = 1 x 724 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 724 is 1
Notice that 1 = HCF(724,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 359, 456, 724 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 359, 456, 724?
Answer: HCF of 359, 456, 724 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 359, 456, 724 using Euclid's Algorithm?
Answer: For arbitrary numbers 359, 456, 724 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.