Highest Common Factor of 360, 936, 689, 741 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 360, 936, 689, 741 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 936, 689, 741 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 360, 936, 689, 741 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 360, 936, 689, 741 is 1.
HCF(360, 936, 689, 741) = 1
HCF of 360, 936, 689, 741 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 360, 936, 689, 741 is 1.
Highest Common Factor of 360,936,689,741 is 1
Step 1: Since 936 > 360, we apply the division lemma to 936 and 360, to get
936 = 360 x 2 + 216
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 216 and 360, to get
360 = 216 x 1 + 144
Step 3: We consider the new divisor 216 and the new remainder 144, and apply the division lemma to get
216 = 144 x 1 + 72
We consider the new divisor 144 and the new remainder 72, and apply the division lemma to get
144 = 72 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 72, the HCF of 360 and 936 is 72
Notice that 72 = HCF(144,72) = HCF(216,144) = HCF(360,216) = HCF(936,360) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 689 > 72, we apply the division lemma to 689 and 72, to get
689 = 72 x 9 + 41
Step 2: Since the reminder 72 ≠ 0, we apply division lemma to 41 and 72, to get
72 = 41 x 1 + 31
Step 3: We consider the new divisor 41 and the new remainder 31, and apply the division lemma to get
41 = 31 x 1 + 10
We consider the new divisor 31 and the new remainder 10,and apply the division lemma to get
31 = 10 x 3 + 1
We consider the new divisor 10 and the new remainder 1,and apply the division lemma to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 72 and 689 is 1
Notice that 1 = HCF(10,1) = HCF(31,10) = HCF(41,31) = HCF(72,41) = HCF(689,72) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 741 > 1, we apply the division lemma to 741 and 1, to get
741 = 1 x 741 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 741 is 1
Notice that 1 = HCF(741,1) .
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Frequently Asked Questions on HCF of 360, 936, 689, 741 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 360, 936, 689, 741?
Answer: HCF of 360, 936, 689, 741 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 936, 689, 741 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 936, 689, 741 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.