Highest Common Factor of 742, 945, 270 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 742, 945, 270 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 742, 945, 270 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 742, 945, 270 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 742, 945, 270 is 1.
HCF(742, 945, 270) = 1
HCF of 742, 945, 270 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 742, 945, 270 is 1.
Highest Common Factor of 742,945,270 is 1
Step 1: Since 945 > 742, we apply the division lemma to 945 and 742, to get
945 = 742 x 1 + 203
Step 2: Since the reminder 742 ≠ 0, we apply division lemma to 203 and 742, to get
742 = 203 x 3 + 133
Step 3: We consider the new divisor 203 and the new remainder 133, and apply the division lemma to get
203 = 133 x 1 + 70
We consider the new divisor 133 and the new remainder 70,and apply the division lemma to get
133 = 70 x 1 + 63
We consider the new divisor 70 and the new remainder 63,and apply the division lemma to get
70 = 63 x 1 + 7
We consider the new divisor 63 and the new remainder 7,and apply the division lemma to get
63 = 7 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 742 and 945 is 7
Notice that 7 = HCF(63,7) = HCF(70,63) = HCF(133,70) = HCF(203,133) = HCF(742,203) = HCF(945,742) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 270 > 7, we apply the division lemma to 270 and 7, to get
270 = 7 x 38 + 4
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 4 and 7, to get
7 = 4 x 1 + 3
Step 3: We consider the new divisor 4 and the new remainder 3, and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 270 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(270,7) .
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Frequently Asked Questions on HCF of 742, 945, 270 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 742, 945, 270?
Answer: HCF of 742, 945, 270 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 742, 945, 270 using Euclid's Algorithm?
Answer: For arbitrary numbers 742, 945, 270 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.