Highest Common Factor of 785, 450, 74, 969 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 785, 450, 74, 969 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 785, 450, 74, 969 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 785, 450, 74, 969 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 785, 450, 74, 969 is 1.
HCF(785, 450, 74, 969) = 1
HCF of 785, 450, 74, 969 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 785, 450, 74, 969 is 1.
Highest Common Factor of 785,450,74,969 is 1
Step 1: Since 785 > 450, we apply the division lemma to 785 and 450, to get
785 = 450 x 1 + 335
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 335 and 450, to get
450 = 335 x 1 + 115
Step 3: We consider the new divisor 335 and the new remainder 115, and apply the division lemma to get
335 = 115 x 2 + 105
We consider the new divisor 115 and the new remainder 105,and apply the division lemma to get
115 = 105 x 1 + 10
We consider the new divisor 105 and the new remainder 10,and apply the division lemma to get
105 = 10 x 10 + 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 785 and 450 is 5
Notice that 5 = HCF(10,5) = HCF(105,10) = HCF(115,105) = HCF(335,115) = HCF(450,335) = HCF(785,450) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 74 > 5, we apply the division lemma to 74 and 5, to get
74 = 5 x 14 + 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 74 is 1
Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(74,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 969 > 1, we apply the division lemma to 969 and 1, to get
969 = 1 x 969 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 969 is 1
Notice that 1 = HCF(969,1) .
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Frequently Asked Questions on HCF of 785, 450, 74, 969 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 785, 450, 74, 969?
Answer: HCF of 785, 450, 74, 969 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 785, 450, 74, 969 using Euclid's Algorithm?
Answer: For arbitrary numbers 785, 450, 74, 969 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
