Highest Common Factor of 174, 783, 735 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 174, 783, 735 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 174, 783, 735 is 3 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 174, 783, 735 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 174, 783, 735 is 3.
HCF(174, 783, 735) = 3
HCF of 174, 783, 735 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 174, 783, 735 is 3.
Highest Common Factor of 174,783,735 is 3
Step 1: Since 783 > 174, we apply the division lemma to 783 and 174, to get
783 = 174 x 4 + 87
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 87 and 174, to get
174 = 87 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 87, the HCF of 174 and 783 is 87
Notice that 87 = HCF(174,87) = HCF(783,174) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 735 > 87, we apply the division lemma to 735 and 87, to get
735 = 87 x 8 + 39
Step 2: Since the reminder 87 ≠ 0, we apply division lemma to 39 and 87, to get
87 = 39 x 2 + 9
Step 3: We consider the new divisor 39 and the new remainder 9, and apply the division lemma to get
39 = 9 x 4 + 3
We consider the new divisor 9 and the new remainder 3, and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 87 and 735 is 3
Notice that 3 = HCF(9,3) = HCF(39,9) = HCF(87,39) = HCF(735,87) .
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Frequently Asked Questions on HCF of 174, 783, 735 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 174, 783, 735?
Answer: HCF of 174, 783, 735 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 174, 783, 735 using Euclid's Algorithm?
Answer: For arbitrary numbers 174, 783, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.