Highest Common Factor of 170, 735, 738, 42 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 170, 735, 738, 42 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 170, 735, 738, 42 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 170, 735, 738, 42 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 170, 735, 738, 42 is 1.
HCF(170, 735, 738, 42) = 1
HCF of 170, 735, 738, 42 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 170, 735, 738, 42 is 1.
Highest Common Factor of 170,735,738,42 is 1
Step 1: Since 735 > 170, we apply the division lemma to 735 and 170, to get
735 = 170 x 4 + 55
Step 2: Since the reminder 170 ≠ 0, we apply division lemma to 55 and 170, to get
170 = 55 x 3 + 5
Step 3: We consider the new divisor 55 and the new remainder 5, and apply the division lemma to get
55 = 5 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 170 and 735 is 5
Notice that 5 = HCF(55,5) = HCF(170,55) = HCF(735,170) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 738 > 5, we apply the division lemma to 738 and 5, to get
738 = 5 x 147 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 5 and 738 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(738,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 1, we apply the division lemma to 42 and 1, to get
42 = 1 x 42 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 42 is 1
Notice that 1 = HCF(42,1) .
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Frequently Asked Questions on HCF of 170, 735, 738, 42 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 170, 735, 738, 42?
Answer: HCF of 170, 735, 738, 42 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 170, 735, 738, 42 using Euclid's Algorithm?
Answer: For arbitrary numbers 170, 735, 738, 42 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.