Highest Common Factor of 70, 90, 42, 709 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 70, 90, 42, 709 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 70, 90, 42, 709 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 70, 90, 42, 709 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 70, 90, 42, 709 is 1.
HCF(70, 90, 42, 709) = 1
HCF of 70, 90, 42, 709 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 70, 90, 42, 709 is 1.
Highest Common Factor of 70,90,42,709 is 1
Step 1: Since 90 > 70, we apply the division lemma to 90 and 70, to get
90 = 70 x 1 + 20
Step 2: Since the reminder 70 ≠ 0, we apply division lemma to 20 and 70, to get
70 = 20 x 3 + 10
Step 3: We consider the new divisor 20 and the new remainder 10, and apply the division lemma to get
20 = 10 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 70 and 90 is 10
Notice that 10 = HCF(20,10) = HCF(70,20) = HCF(90,70) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 42 > 10, we apply the division lemma to 42 and 10, to get
42 = 10 x 4 + 2
Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 2 and 10, to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 10 and 42 is 2
Notice that 2 = HCF(10,2) = HCF(42,10) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 709 > 2, we apply the division lemma to 709 and 2, to get
709 = 2 x 354 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 709 is 1
Notice that 1 = HCF(2,1) = HCF(709,2) .
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Frequently Asked Questions on HCF of 70, 90, 42, 709 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 70, 90, 42, 709?
Answer: HCF of 70, 90, 42, 709 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 70, 90, 42, 709 using Euclid's Algorithm?
Answer: For arbitrary numbers 70, 90, 42, 709 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.