Highest Common Factor of 720, 945, 704 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, 945, 704 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 720, 945, 704 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, 945, 704 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, 945, 704 is 1.
HCF(720, 945, 704) = 1
HCF of 720, 945, 704 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, 945, 704 is 1.
Highest Common Factor of 720,945,704 is 1
Step 1: Since 945 > 720, we apply the division lemma to 945 and 720, to get
945 = 720 x 1 + 225
Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 225 and 720, to get
720 = 225 x 3 + 45
Step 3: We consider the new divisor 225 and the new remainder 45, and apply the division lemma to get
225 = 45 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 45, the HCF of 720 and 945 is 45
Notice that 45 = HCF(225,45) = HCF(720,225) = HCF(945,720) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 704 > 45, we apply the division lemma to 704 and 45, to get
704 = 45 x 15 + 29
Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 29 and 45, to get
45 = 29 x 1 + 16
Step 3: We consider the new divisor 29 and the new remainder 16, and apply the division lemma to get
29 = 16 x 1 + 13
We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get
16 = 13 x 1 + 3
We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get
13 = 3 x 4 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 45 and 704 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(29,16) = HCF(45,29) = HCF(704,45) .
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Frequently Asked Questions on HCF of 720, 945, 704 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, 945, 704?
Answer: HCF of 720, 945, 704 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 720, 945, 704 using Euclid's Algorithm?
Answer: For arbitrary numbers 720, 945, 704 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.