Highest Common Factor of 145, 700, 669, 96 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 145, 700, 669, 96 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 145, 700, 669, 96 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 145, 700, 669, 96 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 145, 700, 669, 96 is 1.
HCF(145, 700, 669, 96) = 1
HCF of 145, 700, 669, 96 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 145, 700, 669, 96 is 1.
Highest Common Factor of 145,700,669,96 is 1
Step 1: Since 700 > 145, we apply the division lemma to 700 and 145, to get
700 = 145 x 4 + 120
Step 2: Since the reminder 145 ≠ 0, we apply division lemma to 120 and 145, to get
145 = 120 x 1 + 25
Step 3: We consider the new divisor 120 and the new remainder 25, and apply the division lemma to get
120 = 25 x 4 + 20
We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get
25 = 20 x 1 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 145 and 700 is 5
Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(120,25) = HCF(145,120) = HCF(700,145) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 669 > 5, we apply the division lemma to 669 and 5, to get
669 = 5 x 133 + 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 669 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(669,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 96 > 1, we apply the division lemma to 96 and 1, to get
96 = 1 x 96 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 96 is 1
Notice that 1 = HCF(96,1) .
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Frequently Asked Questions on HCF of 145, 700, 669, 96 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 145, 700, 669, 96?
Answer: HCF of 145, 700, 669, 96 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 145, 700, 669, 96 using Euclid's Algorithm?
Answer: For arbitrary numbers 145, 700, 669, 96 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.