Highest Common Factor of 720, 865, 40, 224 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 720, 865, 40, 224 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 720, 865, 40, 224 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 720, 865, 40, 224 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 720, 865, 40, 224 is 1.
HCF(720, 865, 40, 224) = 1
HCF of 720, 865, 40, 224 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 720, 865, 40, 224 is 1.
Highest Common Factor of 720,865,40,224 is 1
Step 1: Since 865 > 720, we apply the division lemma to 865 and 720, to get
865 = 720 x 1 + 145
Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 145 and 720, to get
720 = 145 x 4 + 140
Step 3: We consider the new divisor 145 and the new remainder 140, and apply the division lemma to get
145 = 140 x 1 + 5
We consider the new divisor 140 and the new remainder 5, and apply the division lemma to get
140 = 5 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 720 and 865 is 5
Notice that 5 = HCF(140,5) = HCF(145,140) = HCF(720,145) = HCF(865,720) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 40 > 5, we apply the division lemma to 40 and 5, to get
40 = 5 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 40 is 5
Notice that 5 = HCF(40,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 224 > 5, we apply the division lemma to 224 and 5, to get
224 = 5 x 44 + 4
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 4 and 5, to get
5 = 4 x 1 + 1
Step 3: 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 5 and 224 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(224,5) .
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Frequently Asked Questions on HCF of 720, 865, 40, 224 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 720, 865, 40, 224?
Answer: HCF of 720, 865, 40, 224 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 720, 865, 40, 224 using Euclid's Algorithm?
Answer: For arbitrary numbers 720, 865, 40, 224 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.