Highest Common Factor of 35, 60, 69, 672 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 35, 60, 69, 672 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 35, 60, 69, 672 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 35, 60, 69, 672 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 35, 60, 69, 672 is 1.
HCF(35, 60, 69, 672) = 1
HCF of 35, 60, 69, 672 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 35, 60, 69, 672 is 1.
Highest Common Factor of 35,60,69,672 is 1
Step 1: Since 60 > 35, we apply the division lemma to 60 and 35, to get
60 = 35 x 1 + 25
Step 2: Since the reminder 35 ≠ 0, we apply division lemma to 25 and 35, to get
35 = 25 x 1 + 10
Step 3: We consider the new divisor 25 and the new remainder 10, and apply the division lemma to get
25 = 10 x 2 + 5
We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 35 and 60 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(35,25) = HCF(60,35) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 69 > 5, we apply the division lemma to 69 and 5, to get
69 = 5 x 13 + 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 69 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(69,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 672 > 1, we apply the division lemma to 672 and 1, to get
672 = 1 x 672 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 672 is 1
Notice that 1 = HCF(672,1) .
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Frequently Asked Questions on HCF of 35, 60, 69, 672 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 35, 60, 69, 672?
Answer: HCF of 35, 60, 69, 672 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 35, 60, 69, 672 using Euclid's Algorithm?
Answer: For arbitrary numbers 35, 60, 69, 672 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.